LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 1" layout="Heading 1">Q1</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTA==For turbulent flow in smooth pipe we have the following relationship between the coefficient of friction LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNiVRImZGJ0YyRjVGMi8lK2V4ZWN1dGFibGVHRjQvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy8lK2ZvcmVncm91bmRHUSpbMTI4LDAsMF1GJ0Y/L0Y2USdub3JtYWxGJw== and Reynolds number LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjUmVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUrZm9yZWdyb3VuZEdRKlsxMjgsMCwwXUYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0Yy .LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Write a computer program to find the value of the coefficient of friction which fulfill this equation for Reynolds values \342\200\213\342\200\213in 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Program should include a graph of coefficient of friction LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNiVRImZGJ0YyRjVGMi8lK2V4ZWN1dGFibGVHRjQvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y/L0Y2USdub3JtYWxGJw== as a function of Reynolds number LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjUmVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUrZm9yZWdyb3VuZEdRKlsxMjgsMCwwXUYnLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0Yy in the following domain.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Note, because LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElYFJlYEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is saved expression in Maple (means Real in complex numbers) for this exercise we set the Reynolds number to be LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Using iterative method for the equation. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=In order to use the iterative method let call the rhs of the equation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIm5GJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn and the lhs of the equation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNiVRIm5GJ0YyRjUtSSNtb0dGJDYtUSIrRicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlQtSSNtbkdGJDYkUSIxRidGQUYyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZBLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEkZXEyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVElZXZhbEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYoLUYsNiVRJGxoc0YnRi9GMi1GUzYkLUYjNiMtRiw2JVEkZXExRidGL0YyRjktRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GLDYjUSdgY19fZmBGJy1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1JJW1zdWJHRiQ2JS1GLDYlUSJ4RidGL0YyLUYjNiUtRiw2JVEibkYnRi9GMi1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmhwLUkjbW5HRiQ2JFEiMUYnRjkvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y5RmZvRk8tRlM2JC1GIzYpLUYsNiVRJHJoc0YnRi9GMkZaRltvRmNvLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGX28vRk5GYG9GZm8tRmpvNiVGXHAtRiM2I0ZhcEZecUY5print(); # input placeholderNow, Let isolate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNiVRIm5GJ0YyRjUtSSNtb0dGJDYtUSIrRicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlQtSSNtbkdGJDYkUSIxRidGQUYyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZB: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print(); # input placeholderNow we build the program. We set 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 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoJiMxMDEzO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSI9RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkktSSNtbkdGJDYkUSUxMDAwRidGMkYy.`ε` := 1000:
x[1] := 1:
i := 1:
for R from 10^4 by 10000 to 10^6 do
for n to 20 do
x[n+1] := evalf(rhs(eq3)):
if abs(1-x[n]/x[n+1]) > `ε` then
break:
end if:
end do:
Reynolds[i] := R:
FrictionCoeff[i] := x[n]:
i := i+1:
end do:
rey := `<,>`(seq(Reynolds[j], j = 1 .. 100)):
frc := `<,>`(seq(FrictionCoeff[j], j = 1 .. 100)):
plot(rey, frc,color=red,gridlines);JSFH
<Text-field style="Heading 1" layout="Heading 1">Q2</Text-field>We Can formulate the following equation 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 according to shape LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJnRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiRGK0Y5RjktRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZlbkY5 and then use an iterative process 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 to find the value of the real root LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy of the function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==.Art 1: It must be shown that if 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 So 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 When the error in iteration n is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EvYCZlcHNpbG9uO19fbmBGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic= and Find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. What is the condition for convergence of iterative method?Art 2: Offered the following iterative method: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY7LUkjbWlHRiQ2I1EpYHhfX24rMWBGJy1JI21vR0YkNi1RIj1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1JI21uR0YkNiRRIjJGJ0YzLUYwNi1RKiZ1bWludXMwO0YnRjNGNkY5RjtGPUY/RkFGQy9GRlEsMC4yMjIyMjIyZW1GJy9GSUZSLUYwNi1RIn5GJ0YzRjZGOUY7Rj1GP0ZBRkMvRkZRJjAuMGVtRicvRklGWC1GLDYjUSdgeF9fbmBGJy1GMDYtUScmc2RvdDtGJ0YzRjZGOUY7Rj1GP0ZBRkNGV0ZZLUkobWZlbmNlZEdGJDYkLUYjNiYtRks2JFEiMUYnRjMtRjA2LVEiK0YnRjNGNkY5RjtGPUY/RkFGQ0ZRRlMtRiw2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnL0Y0USdpdGFsaWNGJ0YzRjNGYm9GZW9GZ24tSSVtc3VwR0YkNiVGWi1GIzYlLUZLNiRRIjNGJ0YzRmhvRltwLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0ZULUYwNi1RIixGJ0YzRjYvRjpGam9GO0Y9Rj9GQUZDRlcvRklRLDAuMzMzMzMzM2VtRidGVC1GLDYlUSJuRidGaG9GW3BGLy1GSzYkRmdwRjNGaHBGX29GaHBGSi1GMDYtUSMuLkYnRjNGNkY5RjtGPUY/RkFGQ0ZRRllGY3FGMw== When LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is a real constant.This method will converge to the root of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjFGJ0YyRjI= (taking a guess LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHhfXzBgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn is close enough to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy) for certain values \342\200\213\342\200\213of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Find the range of these values \342\200\213\342\200\213of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= and prove that the convergence will generally linear.Art 3: Further the previous article show that there is a particular value of c = 0.5 which will lead to 2 order method. Also show that this method (2 order) did not converge often. Art 4: Try to achieve quadratic convergence of the root LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjFGJ0YyRjI=. For the case of 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 suggested the following method: 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When 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 And LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiNRJ2B4X19uYEYnRjJGMkYy Is an reference function. Prove that for a quadratic function convergence, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiNRJ2B4X19uYEYnRjJGMkYy Must perform the following two conditions: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbWlHRiQ2JVEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMUYnRjJGMkYyLUkjbW9HRiQ2LVEiPUYnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZSLUY/Ni1RKiZ1bWludXMwO0YnRjJGQkZERkZGSEZKRkxGTi9GUVEsMC4yMjIyMjIyZW1GJy9GVEZZRjotRj82LVEifkYnRjJGQkZERkZGSEZKRkxGTi9GUVEmMC4wZW1GJy9GVEZpbkZlbi1GPzYtUSIsRidGMkZCL0ZFUSV0cnVlRidGRkZIRkpGTEZORmhuL0ZUUSwwLjMzMzMzMzNlbUYnRmVuRmVuRmVuLUY2NiYtRiM2KEYrLUY/Ni1RIidGJ0YyRkJGREZGRkhGSkZMRk4vRlFRLDAuMTExMTExMWVtRidGam5GNS1GPzYtUSIrRidGMkZCRkRGRkZIRkpGTEZORlhGWi1JJm1mcmFjR0YkNigtRjs2JFEiM0YnRjItRiM2JS1GOzYkUSIyRidGMi9GMEZfby9GM1EnaXRhbGljRicvJS5saW5ldGhpY2tuZXNzR0Y9LyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmBxLyUpYmV2ZWxsZWRHRjFGMkYyLyUlb3BlbkdRInxnckYnLyUmY2xvc2VHRmdxLUY/Ni1RIjxGJ0YyRkJGREZGRkhGSkZMRk5GUEZTRjpGMg==When 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Offer a function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiNRJ2B4X19uYEYnRjJGMkYy that fulfills these conditions.JSFH
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>
<Text-field style="Heading 3" layout="Heading 3">Art 1</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTA==Having the equation LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSI9RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUkjbW5HRiQ2JFEiMEYnRj1GPQ== and knowing that the process in an iterative process 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print(); # input placeholder we can define 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print(); # input placeholdertherefore, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoaXNvbGF0ZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJGVxMkYnRi9GMi1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2I1EnYHhfX25gRidGQQ==print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1FOL0kleF9fbkc2IiwmSS0mZXBzaWxvbjtfX25HNiIiIiJJJmFscGhhRzYiIiIiRicvJSthY3Rpb250eXBlR1E6bWFwbGVzb2Z0LmNvbTpsYWJlbChMMzIwKUYnLyUldmlld0dRJmxhYmVsRidGOi9GM1Enbm9ybWFsRic=print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=So, 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(); # input 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(); # input placeholderLets first handle the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkbGhzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw== of the equation:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFHLet expand 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to series: 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print(); # input placeholderKnowing that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJnRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiRGK0Y5RjlGOQ== \342\207\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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=So, if this method is converges we can say that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EvYCZlcHNpbG9uO19fbmBGJy1JI21vR0YkNi1RKCZzcmFycjtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRy1JI21uR0YkNiRRIjBGJ0YzRjM=, and if 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 we can say: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print(); # input 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(); # input placeholderFor converge we need 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 \342\207\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\342\207\222 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print(); # input placeholder
And after knowing that 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 we can say that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2KFEiQUYnLyUlc2l6ZUdRIzE4RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0Y0LyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1JI21vR0YkNjBRIj1GJ0YvRjIvRjhGPEY6LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlMtSSNtbkdGJDYnUSIxRidGL0YyRkFGOkYvRjJGQUY6As we mentioned above, the convergence condition is JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYmLUYjNiYtSSNtaUdGJDYlUSJnRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiJ0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjExMTExMTFlbUYnLyUncnNwYWNlR1EmMC4wZW1GJy1GLDYkLUYjNiQtRjE2JVEieEYnRjRGN0Y+Rj5GPkY+LyUlb3BlbkdRInxnckYnLyUmY2xvc2VHRmhuLUY7Ni1RIjxGJ0Y+RkBGQ0ZFRkdGSUZLRk0vRlBRLDAuMjc3Nzc3OGVtRicvRlNGX28tSSNtbkdGJDYkUSIxRidGPkY+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFH
<Text-field style="Heading 3" layout="Heading 3">Art 2</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTA==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print(); # input 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print(); # input placeholderTherefore, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiNRJ2B4X19uYEYnL0YzUSdub3JtYWxGJw==print(); # input 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print(); # input 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(); # input placeholderIf LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTQ1O0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0Y/Rj8tSSNtb0dGJDYtUSI9RidGPy8lJmZlbmNlR0Y+LyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlUtSSNtbkdGJDYkUSIwRidGP0Y/ then LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1GLDYlUSJoRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JEYrRjJGMkYyJSFH(it is given that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy is the root of the equation, therefore, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRJyYjOTQ1O0YnL0YwUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0Y/Rj8tSSNtb0dGJDYtUSI9RidGPy8lJmZlbmNlR0Y+LyUqc2VwYXJhdG9yR0Y+LyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlUtSSNtbkdGJDYkUSIwRidGP0Y/)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(); # input placeholderAnd for convergence we need LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input 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(); # input placeholderIt is given that the root of the equation for whom the equation converge is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjFGJ0YyRjI=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEmSW5FcTJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSVldmFsRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiotRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1FgbzItSSRhYnNHJSpwcm90ZWN0ZWRHNiMsKComSSZhbHBoYUc2IiIiI0kiY0c2IiIiIiIiJEkiY0c2IiEiIiEiIiIiIiIiIkYnLyUrYWN0aW9udHlwZUdRPG1hcGxlc29mdC5jb206bGFiZWwoTDEyMzM3KUYnLyUldmlld0dRJmxhYmVsRictRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUScmIzk0NTtGJy9GMEY9RjktRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tSSNtbkdGJDYkUSIxRidGOS8lK2V4ZWN1dGFibGVHRj1GOUY5RmRwRjk=print(); # input placeholderSo, finding the range of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=: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print(); # input placeholder
For LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= in the range of values \342\200\213\342\200\213found above, will be convergence to the root LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjFGJ0YyRjI=Convergence will be linear for 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You can see that for all points in the range LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIjxGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUSJjRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnRjItRiw2JFEiMUYnRi9GLw== Convergence will be linear except the point 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 because all these points satisfy that the system is first-orderJSFH
JSFH
<Text-field style="Heading 3" layout="Heading 3">Art 3</Text-field>JSFHWe saw in the previous article that 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 does not satisfy the first-order method.So we'll try for this point second-order method.Therefore, for 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 we will get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIidGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUScmIzk0NTtGJy9GMEY9RjlGOUY5LUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjc3Nzc3OGVtRicvRk5GZ24tSSNtbkdGJDYkUSIwRidGOUY5. So, returning to the expression we got in the previous article: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(); # input 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print(); # input 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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2JVEkZXE0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEqJmNvbG9uZXE7RidGL0YyLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkotRiw2I1ExYCZlcHNpbG9uO19fbisxYEYnLUY2Ni5RIj1GJ0YvRjJGOUY8Rj5GQEZCRkRGRkZIRkstSSZtZnJhY0dGJDYoLUkjbW5HRiQ2JFEiMUYnL0YzUSdub3JtYWxGJy1GVzYkUSIyRidGWi8lLmxpbmV0aGlja25lc3NHRlkvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXW8vJSliZXZlbGxlZEdGOy1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGWkY5RjxGPkZARkJGREZGL0ZJUSYwLjBlbUYnL0ZMRmZvLUklbXN1cEdGJDYmLUYsNiVRIkRGJy9GMEY7RlotSShtZmVuY2VkR0YkNiRGZm5GWi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvSSttc2VtYW50aWNzR0YkUSNAQEYnLUZgcDYkLUYjNiMtRiw2JVEiaEYnRi9GMkZaLUZgcDYkLUYjNiMtRiw2JVEoJmFscGhhO0YnRl5wRlpGWkZiby1GaW82JS1GLDYjUS9gJmVwc2lsb247X19uYEYnLUYjNiNGZm5GYnA=print(); # input 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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=So, it is obvious that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input placeholderThe converge condition for second order system is: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print(); # input placeholder
Knowing that 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 we get :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print(); # input placeholderWe found that it does not exists, so for 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 we do not have convergence.JSFH
JSFH
<Text-field style="Heading 3" layout="Heading 3">Art 4</Text-field>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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Having the following expressions: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print(); # input 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We define 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print(); # input 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print(); # input placeholderSo, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EpYHhfX24rMWBGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUYsNiNRMWAmZXBzaWxvbjtfX24rMWBGJy1GMDYtUSIrRidGM0Y2RjlGO0Y9Rj9GQUZDL0ZGUSwwLjIyMjIyMjJlbUYnL0ZJRlEtRiw2JVEoJmFscGhhO0YnLyUnaXRhbGljR0Y4RjM=print(); # input placeholderSo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJHRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUYxNiVRImdGJ0Y0RjdGPkY+Rj4= :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(); # input placeholderprint(); # input 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print(); # input placeholderTo achieve quadratic convergence, the condition is: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2Ji1GLDYlUSJHRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiJ0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjExMTExMTFlbUYnLyUncnNwYWNlR1EmMC4wZW1GJ0Y6LUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEoJmFscGhhO0YnL0Y1RkJGPkY+Ris=print(); # input 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print(); # input placeholderSo, rewrite the convergence condition (and knowing that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMUYnRjJGMkYyLUkjbW9HRiQ2LVEiPUYnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZSLUY/Ni1RKiZ1bWludXMwO0YnRjJGQkZERkZGSEZKRkxGTi9GUVEsMC4yMjIyMjIyZW1GJy9GVEZZRjpGMg==): 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print(); # input placeholderNow, let's find a function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NDc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSUYy which fulfill those conditions:Choosing 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJmdhbW1hO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2Iy1JI21uR0YkNiRRIjFGJ0YyRjI= = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEoJmdhbW1hO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUSInRidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnLUkobWZlbmNlZEdGJDYkLUYjNiMtSSNtbkdGJDYkUSIxRidGMkYyLUYsNiNRIUYn = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=therefore, we get LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElZXZhbEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYuLUYsNiNRIUYnLUkobWFjdGlvbkdGJDYlLUkqbXZlcmJhdGltR0YkNiNRYHMyLUkkYWJzRyUqcHJvdGVjdGVkRzYjLCYtSSVldmFsRyUqcHJvdGVjdGVkRzYkLUklZGlmZkclKnByb3RlY3RlZEc2JC1JJmdhbW1hRzYiNiNJJmFscGhhRzYiSSZhbHBoYUc2IjwjL0kmYWxwaGFHNiIiIiIiIiIjIiIkIiIjIiIiIiIiRicvJSthY3Rpb250eXBlR1E6bWFwbGVzb2Z0LmNvbTpsYWJlbChMNDYzKUYnLyUldmlld0dRJmxhYmVsRictSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRlIvJSpzeW1tZXRyaWNHRlIvJShsYXJnZW9wR0ZSLyUubW92YWJsZWxpbWl0c0dGUi8lJ2FjY2VudEdGUi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUkmbWZyYWNHRiQ2KC1JJW1zdWJHRiQ2JS1GLDYlUSgmZ2FtbWE7RicvRjBGUkZOLUYjNiMtRiw2JVEoJmFscGhhO0YnRmhvRk4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JKW1waGFudG9tR0YkNiQtRiM2Iy1GIzYlRltwLUZLNi1RIj1GJ0ZORlAvRlRGUkZVRldGWUZlbkZnbi9Gam5RLDAuMjc3Nzc3OGVtRicvRl1vRl1xLUkjbW5HRiQ2JFEiMUYnRk4vJSxjb25zdHJhaW50c0dRLGhlaWdodC1vbmx5RicvJS5saW5ldGhpY2tuZXNzR0ZgcC8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZqcS8lKWJldmVsbGVkR0ZSRjotSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuM2VtRicvJSZkZXB0aEdGZHIvJSpsaW5lYnJlYWtHUSVhdXRvRictRks2LVEpJnZlcmJhcjtGJ0ZORlBGW3EvRlZGMUZXRllGZW5GZ24vRmpuUSwwLjExMTExMTFlbUYnL0Zdb0Zicy1GYHI2JkZici9GZnJRJjAuMWVtRidGaHJGanItRmBvNigtRmJwNiRGYm9GY3EtRiM2JS1GLDYlUSgmYWxwaGE7RidGaG9GTkZocEZfcUZmcUZocUZbckZdckZocC1GSzYtUSomdW1pbnVzMDtGJ0ZORlBGW3FGVUZXRllGZW5GZ24vRmpuUSwwLjIyMjIyMjJlbUYnL0Zdb0ZldC1GYHE2JFEiMkYnRk5GTg==print(); # input placeholder
So, The function we choose is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2KFEoJmdhbW1hO0YnLyUlc2l6ZUdRIzE4RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGOi1JKG1mZW5jZWRHRiQ2Jy1GIzYjLUYsNihRInhGJ0YvRjIvRjZGNC9GOVEsYm9sZC1pdGFsaWNGJ0Y7Ri9GMkY4Rjs= = print(); # input placeholder
JSFH
<Text-field style="Heading 1" layout="Heading 1">Q3</Text-field>Newton-Rapson method for finding a given root, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy, of: 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 is: 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When LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHhfX25gRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn Is the iterative value numbered LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.Art 1: It must be shown that for a single root, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy, the relation between two continuous iterated error is 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 When the error in iteration number LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EvYCZlcHNpbG9uO19fbmBGJy1JI21vR0YkNi1RIj1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1GLDYjUSdgeF9fbmBGJy1GMDYtUSgmbWludXM7RidGM0Y2RjlGO0Y9Rj9GQUZDL0ZGUSwwLjIyMjIyMjJlbUYnL0ZJRlEtRiw2JVEnJiM5NDU7RicvJSdpdGFsaWNHRjhGM0Yz Find the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= And LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.Also find the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= And value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy is a double root of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSI9RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUkjbW5HRiQ2JFEiMEYnRj1GPQ== (Note that in this case 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)Art 2: When LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy is a double root, offered two alternative methods: 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Must be proven mathematically that these two methods are at least order 2. With results that proof, which method will converge faster to the double root?
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>
<Text-field style="Heading 3" layout="Heading 3">Art 1</Text-field>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print(); # input placeholderWhen LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHRjRGL0Yv is a single root of an equation, we can use Newton-Rapson method 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print(); # input placeholderLet set 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(); # input placeholder\342\207\222 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print(); # input 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(); # input placeholderNow, we can open the expressions 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 to series, knowing that 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(); # input placeholderJSFHSo, we can say that :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print(); # input placeholderAfter ignoring the remainder we can write the final equation: 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(); # input placeholderJSFH
So, comparing to the given format: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2I1ExYCZlcHNpbG9uO19fbisxYEYnLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUYsNiVRIkFGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNFEnaXRhbGljRictRjA2LVEnJnNkb3Q7RidGM0Y2RjlGO0Y9Rj9GQUZDL0ZGUSYwLjBlbUYnL0ZJRlYtSSVtc3VwR0YkNiUtRiw2I1EvYCZlcHNpbG9uO19fbmBGJy1GIzYlLUYsNiVRInBGJ0ZNRlBGTUZQLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GMDYtUSJ+RidGM0Y2RjlGO0Y9Rj9GQUZDRlVGV0Zgby8lK2V4ZWN1dGFibGVHRjgvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRidGMw== we can see 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 = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEiMkYnRjk= = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
When LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy is double root of the equation, we can see: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print(); # input placeholderAfter ignoring the remainder we can write the final equation: 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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
So, comparing to the given format: 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 we can see 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 = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GLDYtUSomY29sb25lcTtGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRLDAuMjc3Nzc3OGVtRicvRkVGUy1JI21uR0YkNiRRIjFGJ0Yv = print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFH
<Text-field style="Heading 3" layout="Heading 3">Art 2</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 4" layout="Heading 4"><Font bold="true">First Method</Font></Text-field>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print(); # input placeholderGiven the first method: 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print(); # input placeholderLet set 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(); # input placeholder\342\207\222 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print(); # input 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(); # input placeholderNow, we can open the expressions 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 to series, knowing that 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JSFHJSFHJSFHSo, we can say that :LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input placeholderJSFH
After ignoring the remainder we can write the final equation: 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(); # input placeholder
JSFH
<Text-field style="Heading 4" layout="Heading 4"><Font bold="true">Second Method</Font></Text-field>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Given the second method: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input placeholderLet set 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(); # input placeholder\342\207\222 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print(); # input 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(); # input placeholderNow, we can open the expressions 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 to series, knowing that 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So, we can say that :JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input placeholderJSFH
After ignoring the remainder we can write the final equation: 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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFHAfter solving the two methods, we can say that the first method will converge faster because it has greater coefficient in the Denominator.JSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">Q4</Text-field>Suppose it takes to bring closer the function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElY29zaEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RicvRjBRJXRydWVGJy9GM1EnaXRhbGljRidGMkYyRjI= in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJiZsZXE7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0YyLUYsNiRRIjNGJ0YvRi8= using the minimum squares method when the function that brings closer 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 must be accurate at the point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk=If you use the values LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElY29zaEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RicvRjBRJXRydWVGJy9GM1EnaXRhbGljRidGMkYyRjI= in-N extra points (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) must be shown that coefficients of the function that brings closer are given by: 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
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>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JSFHCan be seen the function that brings closer is not a straight line (parabolic function).LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=The red points are related to the function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElY29zaEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ4RicvRjBRJXRydWVGJy9GM1EnaXRhbGljRidGMkYyRjI= This green curve us related to the parabolic function -I%mrowG6#/I+modulenameG6"I,TypesettingGI(_syslibGF'6&-I#miGF$6#Q!F'-F#6(-F,6%Q"aF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6-Q"+F'/F8Q'normalF'/%&fenceGQ&falseF'/%*separatorGFB/%)stretchyGFB/%*symmetricGFB/%(largeopGFB/%.movablelimitsGFB/%'accentGFB/%'lspaceGQ,0.2222222emF'/%'rspaceGFQ-F,6%Q"bF'F4F7-F;6-Q'&sdot;F'F>F@FCFEFGFIFKFM/FPQ&0.0emF'/FSFen-I%msupGF$6%-F,6%Q"xF'F4F7-F#6$-I#mnGF$6$Q"2F'F>F>/%1superscriptshiftGQ"0F'F>F+F>MFNWtKUb<ob<R=MDLCdNfZoj;DP>T:<UcqLjC:=rV_tK?LQuVH`HLjm@n`@>]w]QBy=U;>ZC>hBGemKAHFFZAygb`FdQv`N\\@Nd\\QipxhAPCmkUUQQqOALvYuPv\\MImxH\\s]=nIUsAPXMPVmPpX]w>MV=TSKlkrqwqMWQENQ<RpLwKdNwUyhyO<\\JB<LZ<b;NZ>>[J:Zb_^jioKQegfL=b:BB::vu?gcA@J=J<::j:UO;DTmhtpEUfDJ<\\:R::Z>gca?JB<::FJ::R::Z>;B<::FJ::R::Z>;B<::FJ::R::Z>;B<::FJ::R::Z>;B<::FJ::R::Z>;B<::FJ::R::Z>;B<::FJ::R::Z>;B<::FJ::R::Z>gsja[vWypiwuywxy_vWa]_ZB><:K::sD?[RGYcJuix_SNaC[acK;n:JB::;EN;DoSjYeJGysyyy=xpoLb;N:J:;Z;X[<Nn`iZ^xeYO^doZbobB>\\ZZ;::^\\C>kTHZ^@oS>nSF^:?JJB:ZJ_^ZNg@>l\\pf:pf>T:Z:;:;T^;FdmBJOf`=b`]b:C:>::j\\DJKUP:`LoTJn:J<:ZN:::<;:>D::JZ:Z:;::<::RK::Z>::c:::><:BN::Z:;:;<::>::j\\:::C::L;::B>:Jb:::;<:<>::B::Z?;::L::^<::JB:ZJ;::<>:>B::J:::E<::^::B?::ZJ::[<::>B:BJ::Z:::P>::B;:JD:::[::<?::BJ:JZ:::;::fB::J<:ZN:::<;:>D::JZ:Z:;::<::RK::Z>::c:::><:BN::Z:;:;<::>::j\\:::C::L;::B>:Jb:::;<:<>::B::Z?;::L::^<::JB:ZJ;::<>:>B::J:::E<::^::B?::ZJ::[<::>B:BJ::Z:::P>::B;:JD:::[::<?::BJ:JZ:::;::fB::J<:ZN:::<;:>D::JZ:Z:;::<::RK::Z>::c:::><:BN::Z:;:;<::>::j\\:::C::L;::B>:Jb:::;<:<>::B::Z?;::L::^<::JB:ZJ;::<>:>B::J:::E<::^::B?::ZJ::[<::>B:BJ::Z:::P>::B;:JD:::[::<?::BJ:JZ:::;::fB::J<:ZN:::<;:>D::JZ:Z:;::<::RK::Z>::c:::><:BN::Z:;:;<::>::j\\:::C::L;::B>:Jb:::;<:<>::B::Z?;::L::^<::JB:ZJ;::<>:>B::J:::E<::^::B?::ZJ::[<::>B:BJ::Z:::P>::B;:JD:::[::<?::BJ:JZ:::;::fB::J<:ZN:::<;:>D::JZ:Z:;::<::RK::Z>::c:::><:BN::Z:;:;<::>::j\\:::C::L;::B>:Jb:::;<:<>::B::Z?;::L::^<::JB:ZJ;::<>:>B::J:::E<::^::B?::ZJ::[<::>B:BJ::Z:::P>::B;:JD:::[::<?::BJ:JZ:::;::fB::J<:ZN:::<;:>D::JZ:Z:;::<::RK::Z>::c:::><:BN::Z:;:;<::>::j\\:::C::L;::B>:Jb:::;<:<>::B::Z?;::L::^<::JB:ZJ;::<>:>B::J:::E<::^::B?::ZJ::[<::>B:BJ::Z:::P>::B;:JD:::[::<?::BJ:JZ:::;::fB::J<:ZN:::<;:>D::JZ:Z:;::<::RK::Z>::c:::><:BN::Z:;:;<::>::j\\:::C::L;::B>:Jb:::;<:<>::B::Z?;::L::^<::JB:ZJ;::<>:>B::J:::E<::^::B?::ZJ::[<::>B:BJ::Z:::P>::B;:JD:::[::<?::BJ:JZ:::;::fB::J<:ZN:::<;:>D::JZ:Z:;::<::RK::Z>::c:::><:BN::Z:;:;<::>::j\\:::C::L;::B>:Jb:::;<:<>::B::Z?;::L::^<::JB:ZJ;::<>:>B::J:::E<::^::B?::ZJ::[<::>B:BJ::Z:::P>::B;:JD:::[::<?::BJ:JZ:::;::fB::J<:ZN:::<;:>D::JZ:Z:;::<::RK::Z>::c:::><:BN::Z:;:;<::>::j\\:::C::L;::B>:Jb:::;<:<>::B::Z?;::L::^<::JB:ZJ;::<>:>B::J:::E<::^::B?::ZJ::[<::>B:BJ::Z:::P>::B;:JD:::[::<?::BJ:JZ:::;::fB::J<:ZN:::<;:>D::JZ:Z:;::<::RK::Z>::c:::><:BN::Z:;:;<::>::j\\:::C::L;::B>:Jb:::;<:<>::B::Z?;::L::^<::JB:ZJ;::<>:>B::J:::E<::^::B?::ZJ::[<::>B:BJ::Z:::P>::B;:JD:::[::<?::BJ:JZ:::;::fB::J<:ZN:::<;:>D::JZ:Z:;::<::RK::Z>::c:::><:BN::Z:;:;<::>::j\\:::C::L;::B>:Jb:::;<:<>::B::Z?;::L::^<::JB:ZJ;::<>:>B::J:::E<::^:Br]SZyiyYvysiymyywrPKv=GCJ;FJ::J:;\\Q`<NdmQ@uw=HKJ<qC=RNaKZeRG;>>:\\Q\\<xe=tnyNptMSqJYLc;Pf;FdmR?es:csBCB<<<:<Y>=RNaY>huAPLZ<Xm@jbH]Pf`=^@JZ:BFeDrYTFaxagHaoW?wC]@rGLJ\\pV:POdmJbmRB<LZ:BJ<Vd@jbHQOXuAHLZ<PS=RNaK:iRGAJG;B:ZRP_ZNgHgvpIf>>[Fo\\Jf`=>hKW`:W`<?J=:<<rNEBKUXdshIS^CQZ\\pFWcTGBT:B;JjdT:]tVPsgYrB<LR`OZLW@<v\\pfGA[;NZ>:;>^cO>\\ovnlWyjNZ>n^E>kTHZr@oS>NB:JBZ;Ho<Nn`adhw]@?j:af;Fdmr?es:c;Z;:<]:_tVPsgYrB>\\R`_ZNg@>v\\pFLBZ:;TT?\\RGIoVqQF@J;Hs<L^:^eNa[JaK:\\:>rNFjeH`mytQicS_mIF^:?j:;;<:B:ZRP^ZNgHGfpI^>>[v^_ZNg@V]ZNg@>g@;:<\\Zq\\;``\\oqTXq_GpXaL=j\\Zc:J:K<ZZ`eZidR`oryuEy\\gi[C>\\Z>dZ>^doZBPn`?J:BZJ_QJODtlitu]liLuULLZ<RZ@R:]dZNkT<\\::>_M>iON^exyqQp?Xi]NZ>>[N:C?J:ZJ>>FjlFjdAgsQwwQsPnwG@[J>^J_>>L:Z:k:blCbQEDlOyyuGU=iqKn:Dj\\:::CB<BbSDbocPwgXygfEvXJD:::[Z:TZ_UZiTF_gryuEyDgi;jF::R:JNXKN]REyTiITx@Wi=c;R;?bb<RNdP=\\@:L:;KjsO]dFuyqYUPSwGECJ;FJ]NN?B:Jj`k:yyuyieYyWyyq`s=QeBFZ<^ZH^\\JF`I^unwkF?v:GZKW`RahKW`:;B<SsB[uW[HykuYyU>;CJ;Fjae:?gsaewwS`@rvDJKUPjpLoTJn:;F:=vgEbSCxkWra]iGsV:?B;<KviNjePhMv\\<R:@RAEJKUPRiPKUP:U@D:\\qg<t[<QHAU]YujmJB<<;FdMI=[BB[Wi;FdmBU]GdmBbZ;Jqxyu]Oa]J@qWYHvRILZ<RZaV;tYLUx^iuqaw>lxQ<LoTjwlLoTJn:<ZKWh<yiZ@wQAwdAuK>^:?v^G:aIsuxwSI;gy?[RGAVIgRGA:>>;uV=fUyeZ]hXuykSfGyYCMYvKB>ky_;FdMI@[BB[wf;FdlXQ]tF<DJ;hs?\\R<yyduxaDTqtQLpMI@J;LJ\\p>@rPQJ\\pVjhq\\pfGAsLQZyXyu>qEw_RQvB>\\Z>x:@jbGuiNeP_wSYZAgsAO\\Z>bZ`c:ymNa_]`x@_ZB^_b>^doZUP^do:TSD\\Us`vfDqjUk\\<BqF;OcBkhlYYNUhw]uCoUwihlwrbQuXeIuwyW?B;KBIUCVEiiyYvorY]BB<tK=voiSnXvMeuvpVKUx`=ViuQG=vDiNaMu\\]YJDJ<\\JP<LRdkVUoIyTMTkTht\\puI@J;LJoPJQmwuQn`eosxX]<bvFZKW`jp\\oZEO[VGq^a_s@hEP^:?j:Gj:Qw;NxmQyDn]qqlq@qLf`enarXtXgyRWg?Yhuw[<^ZB^dC^ycquYgxSnuAT:?rfEBK<NhLGllN<LotlVqLEPN:=VL@Ra@TpDk^iwIHLotqxyxFpqGHg;NZ>ngN>\\ovg>ixPaZB^a`>^doZnQn`?JCUD=vD]sv^_oe?ADZ@r?EjOTr_ir_xprEuf@oS@Vf@qqyMeMxQDJ<^a_>xeiyxyrqQuapt]YhC>\\Z>`d>^doZ<Pn`?JFZKWhchwj@]<^ZhCP]CUuHxkwnyhPcHYyyiKrIuu^sEB=b:tyP<LodM?LJ>lXM<<qcDOe;KeK<K^DPMymRaU\\UwfLj:DjQLJe`rEYtpLW_AoseVi\\mUXODmU=GjWgZvIcGieqotmG\\rvb:_tFnxT_tF>T@LJdPQ@u@TkZ<RZqJ;DXdqJNYKiEOdmqyyNotYqmTi<TuEK;LJ>Ls?\\RGQXLuWBGjCQ:<JQZ`X[N_ZFYoiI`wIvv?^;rKQBIeBFYfKyir=yhITmySuMyNIImyUIuxecc:CbSMB\\ovfCWYWR:?rWMB\\oVZSGdmBb`SM<qTnukQqcw[cYjB>\\rnbZIoj`hF>xZYjha]ovdGnm=Xe`_m:FZ<viE>kTp[=FZ<fu?^B;u;ETm;ZnFjuNf_itqampAlx>K=vRCBKUXgigPcHemykYxqmssQuaKrdACJ;w^;FdmXTiGeen:yw>\\RGAvV=kTHJTVt>no@>suneqfw[fiJb:qX<sw>eedwthubrAr=ceTcHyaRWeXxsusueAkhXyRL;FjGb:?gsGr`KY>KBAWCBOe;IBJcPb_cM>q]ndXgiIIgIFW>uH?vW@jMgxTiwJv]r?^KWxY@wOwvmimqIiZWww_^;NZU>[BPmU^g\\xbZ>hr@jbH]V>ZKW`:cFUDrOEZswreunwbnIR>;CfEFjqSnGEwewP;VEkI>?gseYMmRIAxuSxQyT_id>;CV_GZ`QsuxwTQ;hQ>\\b;qaDPm;R^Me:iEkOxdYYHUYBum:VeB^qMFg@weuhZRQjIF^doeYalKY`vqsvixOGi_FZ<v^E>kTx^iqqaw^jxj:@oS^w]@oS>NtLrPM\\TOXuPwIvv=N;LJg`JXIkkTnihW?Tp;QV?eskhSVdQiywFykg`tnDJ<TQD<kTXQhQoaMNjml:@_RygKW`:W@uDb?cOwTYYVtYrsAR<[BTECvWDXmRYUuDkV=grDOe]UerKYXyuSwEUEgcMB>kXN;DosXViTIaRZaG;CLjxu\\pV:b>?rOASsyfQiGkAFPCR:?rlQBiarP_xoWs][Ej?RKUxXgSHuYG]FmuxvCbqen:uJ;DdAhelpBCbyCCBOe;IyJcH=[PPPLBMv`QTI<Vk\\ZRobZFkbvwHa_mApPNxIFZKWhXInrwxQiclQyswc]YlB>\\RGb:_tVGfQ^o;TZ]R:]tF[x>es:ck_`J>es_pp=QVB\\pP<S<IsuXPgHjptUv@ostW=xuwiXM`qxmuMAy^LJ>lTJ<LotTRiJe=N:=V>=BKY\\oV:onLPJQMv`QlEtpbLJ>lMO<S\\EsOImAuMFyjyhOZLWxhSPMQjexQiTtQqLirtUP<\\JPXLJdPQXuLTK\\<RZiS;DdU@fYv_Qf`=^@dJ>es_tp?QnB\\Oi<l@LleTXEyQvhJxaNZLWxTYZlovQmTDYGYpIuvMIKJvp:@oswpjxxa>bZqg;Fdm>\\Pf@::WDRCc\\sYTgUhIRg;wgEBKUxgMhUuBhQyoOykqixQn:qY<Ln`qYuMwC@KVpNZLW@TQhLW@^kfF?tlVq\\??fsFjuPbCQhINg;wgE>KYu^uhH[uoYWO]tvgXUaisCbAaB>esAAww=H;L;oV:\\dZTPoDriUVaUtErPsR:?rgMB\\?sg]hUmik?gsoypousYWT]wVuYyigJ?rY_B>eSaYb:CbhQB\\oVjWb\\o>EW;CTmEwgIhrKBMeBhaCZSTY[rAgSK;DoDVXLyJXQyeSEPm=UU]=m:Yv<L^Ayp:QZB>\\R^\\Jf`=>bKW@D^:j_dJhaKXTSx<p?elD<kThnVXTYawHxUuYTY<rAHLZ>e:_tVn^nqZ>>[v^?OmGJn>[J>^:S@=RFAU`UGTyG>]tfui?wYw;rWsia;yM]eu]eGsSkwh:?gswxxQYtKBa;CBOe;qGEOe;K=j:iM;TVSxjm@lcPJ\\pvNmwUqQfqkYYL>esUqpEYMM<OM<LoTsbdqKDJ<tKC<kTHJv@oS<>jAaJhAKPtkw\\kIlUD=RNaUdUQDqL]yxFPPDuW>=VcEJKUXciwk@Q<\\Jh<KBPmQ<lxeYC@oS<>:KB?YVnYuy=hbGiaqDuiI]uswexN]BxOyXUS@?B;KBWeB>esZuv>es:^ZBJRpNjuRJ@xIPlHUuxpTY\\NdmpTqo[hrPuyxPPn@M=aJB\\lB<yMPm_\\kXaj:DjAdJ>es:tUNa;=CJ;F:=VT?Ro]YrIxxUtXxKdUNZLWpHudHv?pTyCX=dq;n:Ap:@os\\SbiKB<Lr=U:]tFlP:]tF<DjgPJ<Xrg`qXayEDJKUxVYn[yxVXXqquMxw]<NdmwmxlX`j:Io<L^Zwv?gS\\nG@jEiSUhol@t=iJ>dj=yK:QNIxOdmOlHLItO=ywAuKi=jIxNJLKrxxA@X@AKJ<U@=RN_g?@oS>NMuB;iVahSQGEcIV=R>=IvABfKxrQf`QFUCxjQHvqYnAx@;yrMB[?buuYBsVF?JEAKBPm;qTBPm;L]g_ZVogTagOhjX>_JG]Hn[^YxBy`B>kTx`ZpgjqlOxqQGyI`lg?hZ^a<Qp<nwwYshgk?H\\Z>hK?bNaqBfxsif\\pf:pf^hk:XsGWmgPpJYZ?N_=Gr;`iXFy@FZKWx@^tGnulPxqQ_KWh=XZ[I\\Ph\\jwwYohe__F@Z;XKfbbFdm>jlNtL?r_qn_qpS_x`PZ<Ar`X]uHt]GkTX]govGxkLGyuGuGXsnqt>nkM>hiyahWsw>`;hw>^B;uLuYLUH:U@:IB<cd[;rYoXt;v:aIjAc\\ov=;wGsIlOxqQh@wciEs>kdO;XiyUpUWf[c:CbEOB\\ov?=gIyGMcH=lRTAKr`unHudTKWATZPxExqBHq[IJS=xK`RGiJqdVkiNsiYhExGLpvXn>\\uuykTqWITSZUS;DTm<uPETm<B:f[?^iSyUatGyEC]tVaY=wWr]IywsWAbdiGC[b<kwwIFVGH<\\O]<NdmJUENdmJb;ZC@ji>yU`g^InIH^do]tHx?xkgyx:QbFwg??vGGZqqyqFrv`m:Fj_aZ>gSLn`=j`;j`PJx@rqdurTsxio:@ocAVNMKrii_pnqQ^jQe:iqyipKxdJ>^jpp:@oS^wI@oS>nS:JTaT:ylpqnUtVSQn`XPjUq:xuYtWalx;\\JxMLjuwq=NB<LbqOZLgp?dNa[J=ZTacZPwEQimxrp`uGiZvIcGisq>y[yrePywWxAYyv^yrnaX@rlOZhmp`r<@KJ<YM=RNaYM\\w]iv\\pF:RmCbdwGaisXSuluHQ;DosHYAvAwEiOwqiSKUx[icnIxEQCrwxiSiokD@=b:iR;Cl?=oIyOMdP=\\`TA[r`unHudV[g?^Jgx?`q;YnTOv[PZ\\pv[X]yAt]wdwqmtIxxny\\>bZyyxApHV[<^ZBR?VjWX<L=CBKTmgP`G^ZdDZiCXctLsCO;DosCWAyAoEuOwqaTKUx[gCnIhEICrwxish_kD>=b:Ye<KnqDrxlUhLW@:Zt@n:gtQnw?v]GQlB^yP?bNahjnmL>otiyPyaTpyNq[tauO^ZVYyQ?u?VgZ>bZ_b:_tF^x>C:\\>:Qb<cTYMhQ[YnSS\\;FdMI=SSC[TwqYeKWhchgoDmCU:iiyMHrwc];RZ_U:]tF;S?es:Jh:WcB[TxEhX]vK_G=?r_EByMl_MOi\\qS=riirqTJuUygdJVYyq`uPuK?=vbDJKU`WQn`;jPs[CbDyGHqywoWIcW\\wcgSDJcHEAGwGT[?ROywMibEMxP]BP_DjuwYMXU]GD?B;wH>[RGyHjoYv_TNa[Lqb:iv`hsPGebYb<fdYolwY^Ix[g?nIh_O>\\oVCuWP]FJexuaXKQXvgC;gV?[=B:hBPNNyvQHkTH::ncP>x_Fil>qIXg[>^dopRqn]y\\cyxiYvI@Z:x_>^uui]GNZ>NqEb`tZTH:TM;tlUpPUeV[Xl?\\YclmFlw]QUB<kThOpHwribuyxkyb:>jbHW[Zc@jbH]f_obH=BBOegmhDQRa;CrQFvCBSyRnoDJcHUuWYIdEwxuQyKWuhIf?eSa=b:CbGeB>esZUV?es:J\\n@V\\>^isim:`w]NeE>KUwgYIlExxuUyKXUiIn?gcaCJ;FjGg:?_kPn`?JBdmhSQGEci;=rQguU;TwgvPQJGioqxXeyjePywquy]xgUw]MpwYrsxxiuq?qMJ@rpQJ\\>fEhbG=Z_sGKBOuUluWRMeq_Fj_f:?gs_vp?UNiB;OgYyw?esE;uXMhf?buhVqZjCJRwmAZE=Dn:etQXu<iNsUO<dO>\\RGqLUaVKxL>\\yV<q:`v_TuC<qqyWqhnX<k:IX<L^ZWs?gS:j;EJY=VADJGXLryl:@ocAMfAOZyv=qkuPwSnc:iqYIqZ>bZXq:@oS^wZ@oS>N>Va@cEN;x_gXJ;trCBKULjHo:xmITmh]oAQyA@juuq=ER:@RqEJKU`=Pn`?JC?ZqfZvGcwW\\FYsC^eJ>xaf`i>^sGcuGZyvaTyg[xZrQb:iqYItZ>B>OSA;?:cYM=rQOtqCrv_e:iB;CTmQBLwdnwDjYx]gyPKY:CTMIEZ;RZUT;C\\]gbGA:RNaWmgTPPj:xO\\xLJ`q>@r:@jb>ZIAgUGZyVeTqgWhjyQ^ZquiAcJ>^JMdmJu^T[@[mnb?oUJ;x?Yx<KdQ?DR;DJcHA;xFohO;xmgfgqtS=ibGwFbS?bbGmJETm:K?v[<nqjOaX^Z`A[BPmm_mwOstOZxosfxpandnqq:XiyYy`o^B><QDJcH=gyJcH=:JOdPWHJ<tkE<kTxkiEj?\\Q^<NdmQ>tw]US?\\uuYSsdqSD:[B>HJt@oS::IS:ydEur;?rmKB\\ovmkwxcXwCBysbPYuMSGteGZquyQuBYGB;DRUU:]tFkxA]tF;<ZWvqJweZvkyN:gB>[RGiBpCrLkdN;xmKWCiWk?gY]BVYyWCC<[BtWCBOe;qCDOe;K=kGqNo]y\\dY[]IxA?Z:QZ<NN?r`;U<Qd<kY@eGsgGPcFdMI=R`;FdlPN]tFZZZdXfQNwEPvkXeiIrQ^\\Jf`Q^uNVcTob:ysehfpPr<oqJ>hiyhn>[J:::VFhNkAE:::CTMI=::ZWVpJweDvkSQgINuJ?bNagrHgP`yR@JIu]]xx;UNaX@;CJ;uN=RNaKf@oS<><NdmpSwrf^tQ@r]opTYjp^\\Jf`UngTh^yn^ZyvSYfnqaR_tnoZB>\\Rad:_TgcOcH=[@[RGqHUehwQRekiviWI_v;CCv[GZ`YrUJv]YeEJytvTuWYqLExXiyu\\UMw\\J;Xn?\\RGAVuiRGAJG;UegOuxEfx_wgui?qEjUB;Cl@TmbILXTLjYXhIPtuMvyW;txxuR;@J;pw<BRIZ::i^Ugp_QbAwqZigCPv[@[f^_ZNgh^qsnlPQc:ysypdUipGQfWYyqHuDw[<?vRGZKW@oUNaCJBjjpPUbxOmUUgunAHQB=RNaQbUpwLwNDjKymAxQ`ynfltA`pQ<XiyWyhjXFj]iZ>CrKB\\oV:o>bght<uRy`rgej[IVB\\PL<LoTMgml_ppJ<MwIYbLWp@u`iVPDwXyqFqTR=K;LJ[@Zm>jMf@c;sdUoHUetxE^kWgI>v;>[f?^ZNgh?pCp][Gg;vaevlXqmpYkmwwiwq?p]:@rkQZ\\DVCBKUH::ftxGnx@ooxu<w[:?vu@ocA\\J>qQ?rIQsugiIwiqwxxYtI?jay^Jye:_tFnxJ_T[@[=pXEdMwQV`yMcXWqhvP\\Y:@jbHY:qNu]rAiJvayv]YElpW=juuypXUeIrB\\M]<^FnpT_T[@:dx_`oWqlS=P;xl<Ln`YS\\tOZ<Pf<vayvjDnq<y<=rwxuKAN:=nu@jbHMfAnb>B:Puf\\XnYsRUmAdpJMJALKBPmAlWtxRx]UZ]xaQoyMx[Ixg\\U`EJhiyEaW?hjJ<NJLKBPm;\\mbH=:plX=wbyLhhnYls\\AKJ<yU=RNaXR<KvTOjLymqx]muYuvD<qqymuxxX`m:qO<L^Zw^?;:eGw?tKyGSUSy[e?IDZ;FdMI=\\O\\<PtYxP]tV]V]tMTmjuuy==xxll:ff<NN;TDOe;K=RpPlEdMwQXo`v=EUNDJ<tUD<yMPmHtJ;hP>lRymytyRLytRyrSYojuwYhOhYxB<LbpLJdP=DTKUP:[EicUdP_UbAwQOg_sEDQfB;DJcHWGB<ScE[cxayOcHQsuZYePwvXyYM[gqgn:aP;Dd:g_do::b?ocxEcTMv[[G<?B;?U:yeNaccaCL;iO=Vnyvm?ssUwpaGmqvhiyEPKEDN:=NN<LoTJrDTm<B:DpJIdTplr?[E@^:?^PRGAeHAF;WU?kRymIEOeqoWIQHimwXyiFqTR=C;LR;DTm<jMdP=\\@:It?oTvEUt]x;[YrCB<cF<Kf`EC]wH[;Xe?bYGuqOxpoYmuxxqtUyVkaBB[yE=jS\\M=DTm<B:oEW=gi;SIOxuAX<SsB;cTWsfeb?<x_@jYHuHtrQMJhgmGN:hZTd=ds::JwEn]xUDpni<uALLZ<Xu@jbnh\\w]:?nF?fnyvrxi^fqfW_PHi]vxxifpPRKB>KR;CTm;bMcH=[@Zqx_NylYXuChi:FjpQZ\\txUCw;r;QB]wIayC`Wu`ItWYyqGuDuC<=vREBK<poQn`;jthY[XnYmXvIkHXuq@sA<Lr]U:]drq\\R?Z;@eZ_xaaivIr@vlK>hiye`W_f^j:FjJ?BSBrCTmpF:qhJILlmQ`iy?Gjm^Z>gsmnxSYdhi_JGxmwuIqyXxf>iqyxvxHeoFZ<vya>^doZaHbNa[J=Zg^p\\YsGigEXx@aZB^__>^do_oh]PVbZN\\b@ysx_doBYv=mwwyciEb?;DZ<T:]tF<J?eC:dTt@dJallOimrkKB\\XVpPu=pM\\<PtuMr\\jcUmAaXiyu`UOw<K;XV?\\RGAVeiRGA::rbydRsqShnUIvGAKnHLJdPUO_Ef^jGcZ_xxRtADiKU@=rwwYS:B:W<:f^Efx_in>HtU@\\rnd:_tvnheiarI^<nwCVii_puwyXYyeIwB:GrhS[b;s@_V[oif_djKYMKBAQCBOeAqWwwBy[R:iI[uwGoXiyuuuYwcE;WD>[RGAVQgRG:WMpPOT=wbylMty[<jBhuJDjgeJ>WuhgoAV^jYl:AwwIZaQm<nwwYghYkOG\\Z>hW?bNaqhgxqY_?gS:fxpQbwG^sWmFAZ;rELn`XN<=vvDJqIkwmxViaxVicIcB^md>^doZuv_doZb;jUYKoiN^iWlTJ><KBPmHAJ;LJy@KrxSfYX^\\uuyxSYSIMRZaT;DdjXx\\pf:pf^DZJw`UbxOWtOC`q:@J;HR;tYLUXJ<trDj@QJhIMGxPiyuEuXiywyfa;FjMiZ>CrCB\\oV::TUoQX[pqf]q^Lx<LJ>lJ?\\RGIR:Uv>LME<qa]PXaQKUpyqvsMJ<\\JxQLJnZAFbN=<kTjEijtQlKyYIdQ;DjhLJ\\n_uffW`Zhy\\jwyrxurPyM^uuYo?gqYFZ<VP>bVC=[@[=DTmxyPEY<LJgiJ>espYUbIJB\\lC<kThVNXtXAswxYTdpILN:=v`DJKUP:hLoTJnT>lGxSEdx?MnaqqSeP;pw<buqCTuQoPJhYNopmqw`qqyuhjwxa;NZqW[BTZ[GdmBbmZZQHGM\\pVIiolPW<TUC<kTXUgunAHNj\\OZLWHTLHeY=txxIoVqQFNZq>[BT:OGdmBb:nyT?oiv[wpxEQgC^w`>>WigAgaIFJUGZqeLUwSeyhmwwit\\ouI?JmhJ>ChKW@;?VppqdsQhjpxxAeWFjMa:HWulwsEK^MJ]xxQxMmIuaXmtQS:iamHb:tW=jS\\wZ@_:cnbSUYeoRy_DfgynmTA=b:uH;CLqhMmpU<tsB\\kXyU>esumxGiqyqMQuwD=j:aQ;DdZg_d;BeqWOAwQKboueFQsB;lO=RNawtXXPiSZIQ;txSxvfyYwaVqqyomx<QSB<LBaJ>es:iSNaKJ;tXe`YC<UquWf`k:I_>sNieqau>KX;sxS_uhOYLiiyOUNYyK;FjSU:]LBXkTZ>JeaWOXSyQQuEV_\\JB\\yX=RNaXl<KJ<MO<XYIMO\\saiuuYXuTl><KfHNZLW@TyZLW@:`omhThDyeaw?hlJ<NZ^HKJVYNZqqmukeilqeXiyq\\`vo\\JB\\of<NdmJuXNdmJb;meYQGQWyayx:QCB;DroFZySdmUmMxdKB>kUE;iyaipKgxebuuYo?gqYF:=Vp?bb<LQd@BhlmYQOQPyayx:QKB<LrpNZLWXUXlQO<\\JXUKrxyvpPdpY?XYye@::ZXHudv\\syfViidFZ<Vf<NNkvaMe:CbYYCrwDGIISkwwYXVgYDCB<sxC;[pPn`;hv`mwPEqnxsoqxc]JB\\tD<kThpXpuG@J;xm?\\uMpwwDLhiyqQytuX<\\JhyLJdP=TVKU@:FeYXW::DTmmvS<Xiymchwm@KJ<q==RNaKNeRGA:juupD]rvxtQYqM<NjtT:]tVXwgYtB\\mh<vXdTuMJVYyeeQwXM;LJmiJ>ShKW@;?Vhiqds`kYYweiuC>\\RX_ZNgHixpIg>ncQ>hIPowFZhiyopmXik:FjsQZ\\DRWcT:lwSQoKYSryrvxqB<LZ<pT@jbHqTqkRuK;hy?\\ucPwpAuwxqHQtuDLZ<xF@jbHMrXkT:nwSQ?[yXsTiQS:?rmOB\\xVwiYtDjMdJVIodOquwiW<::btigDuGYixeCxH_BB;DbgDJcHeeIwWE;KBiYC^wxfwEmuwyMvxSDhiyua?Zj<ZGgyPgnQhwtilrwb<^ZB^tD>kThpXpUvx?NtuolbHywYquwyuyvGaZ;NZeG[BPm;qiBPm;NMjkiolEqXtPnqK><KnALJdPu]wMhTL<Q;=rwYwwiUpuwyuuFaJ;LJeEKBVjwA\\oVZn:DyPekVmnmySoDc;NZII;ovmmxxCe:CbigB@mw^uFwICHuxxuiD?CJ;wh;nFlhbH]ZH=r^YUoKX;osyct^CB<\\Qa<NdmQauwMHKJ<LotRIAjuuyb@nsMJ>lmP<LoVaZNg@>G>QswgetB=svAeoyD;KJnmLJdPutwXhpM<uY=rwdwIYYfquyxyiHJI=SZuX;DDAhbG=<bGYiUgvl`yXxlQW\\Z>pQ@jbHqQqitO]<VqC>qaHkTXqWHgIYB;xm?bbGEV?CKUH:UHLqjbHYgUoLYSlipquxdLJ><[[bTZ:?vygZLYyUqoyqmGwxxwql>[J>wh>^dsHKcT:logeTtEOxpxhqU?=j:DjXLJ\\n]uafO`ZB>kTxquVZhiyxgfJ>^JiElZJ_T[@[mvqYePtBHqeyuSyWm=ng\\l:DjUeJ>wplQimOZ>ngL>hiXyY?eqqyUp[Rxp_>bZOm:@oS>dEPm;:vaigtbinQyiF>oGItq@d<^Z<FZKW`:cJ<VcDjKYqXQTITx`QVVYyYaJmQX<^_abThOKd@ZBPmgo[ehjL>^jAq:TxkQf<j:Dj;EJKUTL<MvLR@IKJ<YJ=riAfvGdm>B_PZLWtylByps\\oPLS:@r]QJ\\vrqd:KB>Kc>kSFWehiy?ubAYuJ;FjAe:?gS;tEOe;NU:Jr;Z?O:@KLYuJ<N:=V\\@jbHMZUkTH:ncHPmane`WuV^cEf^:?fCGZKWhCigk@_<b<CbnqUR=xKYtXQv^YYyaH^uE>=b:i?=reKOJa;[evEiCuGioyEsvgmcqgbL;FJ]GZKWPSbtUI<[BPGDBuw?WsvXKEDQsquyEjAYSB<Lb=NZLW@Tm^LW@<G\\mpEqCuOfPR`Um]dW[`JB\\ub<NdmuBXwgHKJ<YV=VqYY\\IWqqyAyKNhJJ<NJmOZLW@\\n\\pfGm:IWQXmWyOehgvV[_BbEGZKWp_upSc`;RZQnWywCxnWYyilWuxlK<NJAS:]tFlPE]tF<DNs_qfqYcdWm=vf[`ZB^pP>\\oVeiwM>hK?fQYi]I_qqyEXufif>>[n^\\Jf`=hcMf@JuxUhMtEEWUhKn@T<\\JB\\SN<LotN\\UybLJ>llK<SiYlehyeYkpuqqyOm=Vf\\j:DZC>kTHZg@oS>N>puiv`fq>ppSAbEf^:?j:]mO^pxk\\>bZG=ciIMcTWsfEf??DZ;hC?bb<uBETm<RmBjWUNau_QtSqv:CUbCB<sRC;KIPuhu[:rM?rbiEmYVxIwyoXuwxycwcYxC;DRwGZKOFiRGAZKlWqOqTnQlspTMaEn><KJ<Y:=RNaY:duAMLZ<p>@rbiMM]tVMVU^Z;NZGiZ>CRARKUH:jHEdtGufWpSo\\D?j:FjAhZ>s[iCjIx>^k:Oiiaily]CwucqUSXJ[G>?JMeJ>ecq@oS>NrnEiCuGQgWpSs<EK:Wr<Nn`YrU>v]I[J>e@kudRGiVp@t<=KJ>d:KUpNdmJbmRT?wVf`une`VuV^[Ef>vg>^BIhZ;R:x]nOqIphxxxuvh>>[J>yJ>\\oVjm?>GBTBWwGqcehCdgmC>gbL;^y>[Bd]IR:?B;CTMIM:@J;xn>\\b;`qbH]Z\\JI`dOkShgHxl?P\\Z>pSDdmWpGfXsb:CbLEbKYIdiuyIH[ocqqyLiClqV>;CnwDJcH=gGNcPb[lGqSfq^npSA\\Ef>Nr<NN?x`AUTCB<SKRexXQu_quy`s@MUBDJ<TsC<kTHrP@kTHJTJWmOqToXmKUaWnhjL<^:Gj:@oS?jbi_B>\\RqeZgtuWgQXiyqxA^r=N\\Z>\\E>kTHZW@oS:[gxEiSexL=u`Ubg[d:CB<cb<Kn<]SieR:@rkLJe`uauTyxxYTXZ\\QbDZ\\SNaCbaRGA:ToYmWPEq>lpSATEdN:s@EBKUx@]UieS:?rpOBe_uauTywxiUY:[IRCB<cV<Kn:PTNaKJ[div`fqvip;xpJK>L=h[Tt>;CfriuYFicx;sdwxxItaQHI=b:\\J>GrXWkTH:]^epehOtEweU>iEf>;n[@jbHujUtfDm:Dj_]JLYyg@os`sPLUBbAgB>esZUB>es:ZCPm]xlvxkswiKJ:=vXEJKUxXuUiqS:@rsLJ]xXYaRdeluuYlpXm\\JB<LrALJdP=XXZLGBPEiVacX]w>espsRHQRC;Db]GZ`WvHYPpc;hn>nbiUlAHe_uuYdoWe[@J;DTm\\Q=Ln`=Ka]o?@rDtlU`xLut<<u\\DKJ<NjHl:@osHt`MYNLJ>llJ<SiIrCyQLpq<iqyEKnUkZ<RZho:xQc>utFdm:;Y\\QXmSxlqt`UFf[\\BB>[RGqBU_VC_JbeOJpuMxov\\xMtxxYOeQxTLJ><KVeLJdPiPSwMYW@oS:fctGeEoyH`hUhkj<:N<::f@:N\\oVZcV^WfZ`oehOToF`mXvCUPaS:?rHOB\\hMqetmDLZ<pT@rbimsYoyutvasuuydmnPYR:@rXLJ\\>fYfyCgSUpGFmQXmKY[TW]NW[_>b:@r`LmUtGhxR]JB\\O_<PtuVPdPQPuHUk[<b[@jbH]ZOkT<?rWITm]xLmt@Kt<j:DZ`IZU`wKF[J>E;gxwRYiYiyU@ks<=CJ;uP=RNaCpoTNa;nwEicoiffh[fhjL>^:sJ=Z=icoAc>>;QCNuu]wwxwxiSCcEV>;CfUFZKW@SUcKW@JrXwlUTwEKeUJdEn><[jHp:Th]isoEG?B;gv?[uiwdYQFE[F:=v`EBK<JfLW@<G<kTR_Ef>;KjAq:Vxki_j@Z<^ZHn\\Jr=wHYYfM;Fjyd:?Or<K\\pfG]dAoSpepPu:HebFZ<^ZH::_c:MYYqykshFYbR=C;KB>kuN;Dosu>Sye_ByUypQxyQbqgH<=VCCbKAgsKYcOydyiHAi>kc?=L:@ZyF[Bd=CR:?B;gPFpu?yttMMeHN:=j:ym?\\b;I[Kf`=^@^BgsPEM<\\:sDJcHYsu<SCZ;R::rCMB\\@VqhRGAJGkK@oSpU\\PuZAUbDJ<\\JB\\y^<NdMQJ\\JB<LRUTZdqQXyAMtQauIUo\\<RZyx<L^ZafBPMo^<Nn`WmgPpJOZ>BIWCBOeIwW;gBJ;F:=vqOB\\of=GR:?rCKB\\n_EPMjqMn`XsLUmgepJM:kWK;DosW[ex`_BB;Db<lXYuEyL\\iKC<<[DJlJRPn`=:@ZmhsPGebF:tkEf@yh:QBB;DZ;XC=RNai>av?]BB[HM;DoSbGSDoS:\\UCPmcinByq]xnGIPj@T<JL<\\XOflQ^<^:SSB;i=yGkgCPCR:?R[?bbGEZMcTG:\\RGqPUefC><[Ih;Fd\\iR?:LJQhJ>esEaTX=S:@RMDJK?pKOn`cSC_e@oSpe@Pu:>ebFZ<B<sd?[RGYsNmUB=b:Cb_aBVYwQWuLSC\\;RZiS;ClU@VYtOQdP=ZvQ]oVtEqky_tvhsPXebFZ<bRV``X`B?j:Fj__ZVyxQHuDV[[>bZic;FdmicjFdm>ZmNtD?bNagohePVc:@Z;xb?^BITxuEH=b:dN<Ln`EK]xP[<RZIJ;DTm<RqyNo:\\miaxlUt`IRg\\l:DZB^[E>kTXr>pu:@Z;rLMBcyX:wcssYK;F:=VpnfZn_d;\\B::Z>Nc?^bGQdHwg@?j:is<Nn`?ZfNg@>GoD<sEQ?eK?gSQv[cGL?B;KB>Ks>Pm_]lXAk:DZPP\\RFkUpyNqvLWecG`>npP>\\oVjgi\\oV:pL<L^PVu^Gl>>;kdK;DosdSQCEF:Eg:?oNXtUHLZ<XM@jbHM:QkTH:Qt<kGgSSiuc?IDZ;RZEU;CTmEugGhjKJJ<OK<xwDn>HtU@LZ<XM:ZC>qV`_oh]PVBnp<NNqXeaGV?B;luP<MwqK[yMEuYU`u:DJ<tO>\\RGAvB@kTH:^kX?cPPiRVk[>b:@Z;xr>^BIHtuEF=J<Tt?lRyXRBPmMypFyJL<uX=RNa[kT@;ofDNZQNl`rp<U>D:SuB;cTWufefACF:=jEQJ]xuclOy=lQL\\:@rEFZKW`rN^\\pf:pf^G[;HtE>kyXqt`rpNE=J<TsBf`QHuD:;HG=VnYI?ah?OyZKB>kPZLgp@eNa;lMQ<SitMIxOVQJB<LZ<RZEU;DdlXe]Gf>>;kfC;yXGHGOuACDZxL;Ddj_^>gs:fsBYv<n_UvkiGj?>\\ZBRqS:]tVqWEeIJCB<[BXqDjiI]iWlSB>;CNCKoTJBEDNq:Ois@ykv`wGrx>l:F:CbpMB\\oVugGm?V<[JrhS:yxIXubeqkDJ<tUB<kTHrKALoTJnnnE>qN_cavx;`ZBBHWDJcHIWuluk:bicBvuyj=IB;DRgGZKW@Kv\\oV:Fg<n_MVtbhiJF:trE<[Ixa<>ZB><[yP=V^YICKT<[BBPOZLgdfxcih\\pf:DsgTZ]vLAvy?WxUwPAYmMB>;CfeGZKWheiwoEH?B;lj?\\YIEM`\\x@\\JB\\y;=RNaKHxjbHMZNhe@jEQrg`qXam:F:tUBRAUb:\\JB\\yC=rqaLaYj:DjudJ>Gjh@oSR@mWK;XC=i?gtUODZ;R:x\\xYyynymYyAyyCPmHP[;NZ>>[VG<uWsOf^iH>;CvWGZKWxWGpygQYcTGZhG\\jGarhjOYM>j:@oca[JBJ;FJ=GZYYEEF`wP:@rYQJ\\>vj>kTH:Do:MYc<OW]jqTN:=j:vrC^yrY\\Txmyan`ykyyw]A`v>`;NZ>BK?RtiU`YxV]x;qbB;DRq[m>uLGdmJcdLBuO<dnE@x`]JB<LZ<XV@jbHYVqlu_ZBBDiBLywlKf`EyP=Y=MBgiB>esZUC?es:ck[DJy<yA@yFTLZ<B=TZytRGyawyqAvAEEa;R:n[K>]wqkm?[Mxr^>bZy[<NNlM\\pV:B^;HtYByYVX@[:?j:BO;DoSTsSX>;CJ<veDjKywr\\VC<LZ<Ndos:@oS>NMV;_xAgYvIb@CCJ;F:=jY]J>ok>F:\\JhqLjiqaqW[uwI=VyDJKUPRYTKUP:U`l@btYrvyrVivINx<OZ>B>;CV]DJcHiKRsEM>BFSCrqIn[SbiCB[E];FdmBUeGdmZs`_Zyjrifdv_^>B@r^DJKUXL\\pIHN:=j:vuww]l?[B>\\rP?OmDeYtembJsEOZyjqYS\\t_:@Z;r=MB\\xjZiYfD:sbE[fYIdHsVmAy>kcK;DoSbgoDo<W@mUD\\ny<pwYVayOceq:@J;LZFN;ovZTv><KJ<NJDK^xuKPnITP>=j:UQ;DDEebG=QTZcy;ewy?WhATK;F:=juhJXIkSxqxpxhipsuY<\\JB<LrtRZ]vuTliiSaamMtStmm:@oSVhKW`:cBOeHAB;KB><Wa<NdmpUQPElN:=j:ql<L^gvpOYbK>]P>\\oVZ<GdmJsIS:yK_uJ<Zn?\\JrHSi^ec>;CJ;II=FwqIomeNwF`;hq?bbvq\\pf:DKcHWGJB>bZhm:@oSqgEa_RT:XN>\\RGYNpHu=MLrEOZLWx`NtyvE\\RGA:yG;sIveE>K:;UO=V^;VXeeWexSigE?B;KB>KyC[fYigvybPUygihOSDrQS:>aUNn`?jp?xBx]pxZioqAw^:?j:QRitJCYaYwPkvk_H<[ZZHk:xwUgcpNslF[VA^ZNg@>o\\pf:<_w;Yei:XQ]evOyxX=mAQtB<LZ>bMFZYypT`gNhfL>q;?bNa[JgbGUu;X>yCQYBqcu]SDZ;JMvd]XvFxtoF^m`c<^ZBBT?C^wu=Qevke_MDZ;xC=RNn[\\pf:DrKdxAHoywrEIjAhr]V<[BB[SP;eKSGioY@avAuxk]BB;LZUX;`xu=u`aOXtk:ql<BRqTKU`ZH\\y^bINufwkD?j:Fj`PZQWj]ydiXyvAuOxwOalMQpC><;DR]SZcyHmxsmWkwRl_E<[BxUFZKW@sr<]tF;tHKECuY:oE>]vKECJ;F:=v[EbDADSEyXuCm?yrMJJr>=FwqS`KWhMX:[I@IH<FrPWkTHZTqr]Vny>`qnnkAg>>[J>^j@o:AgB`oVxeN@sl@[J>^:sB=FwhW]LJIPRZUS;DDUgb<RUAY^dy;DwYimsHx[@xb]JB<LR]UZPPDmkxxt\\aTPxR:@Z>n`J>cyXpg?xbq];@rPQZ\\lXETmRtKvAWv`WEeIhB;DZ;X:HtRDUktY:TpA]N:=:QR<CwqyHy=F_EfG]hNKBY_B>ekk=LoTJnhS@]yJ\\u^UNwlJ;L:ky[;TKCGYeiAkX<[Z:d<?biiXe[w<gHJ;EQ;Dolj\\pV:ppCAkYlYU`W^xrZ<R:bbGwF<R:@ZAQ[rqeq_wPYijis>^B;uJETm;RemI\\ybXUxG[hvMB>>^L>ioy^ivynyqAw]b?k:F:CB<Sd?kRxWwGmUdwc];RZyD;pVj]N>es:dosAsByKtxkSuYK<N:=:uR;nkupfGaZB>\\Z>xH@RiUiieIIxT<KNYKBPm;HobH]eOa\\yZVWtGXpfOZ>B>KS>[RGQD@`Z<JT<KF`YqYxADUT\\WjhNhEOZLW@TudLW@<WGuR@mYjhPw]VEqN:=j:^Zxq\\Jf`WnZ<^ZB>\\rfbZ_vuxmbHiDI_kameH[BTjWF\\o^]H\\y^sTfgPhnL>>;ND@ruDXmMs<`YBD:<LrHUZdyX=YmQpvhQ;LJY`J>eck?\\oVZnpZ]nibg`Ra^E_^:?J=vKCBKUxKkXYKS:?J>lMP<SyXNxmmu=yK\\YvDjghJ>GrpQkTHZTWjK`xAnd=xbm`b<^ZB><[CC;KA@yFT\\:LMGwq_bKWpcqjUohuF:\\WS@oS<ng<Q\\yJNQjUPVC]JB>bZGCHq^CDL:kFE[fYIFasGMyrK;I@=RNaKo@oSJLpy:MxqeuP\\uFUS\\<R:@ZqP;XEaM<\\ZbC^XRpDYvTs^<tH=BSU`KW@pLUDSy=MwAmU]wk]OA@J;L:kWO;DoPseisC<LZ<RZHm:xwMhsp\\slupO<LoVeeNg@r\\UFx=Cgkh[kd==:SSE;cTWSiuc?<R:r^EBYyFaSbuAI<sUB;cTXn[LW@<WE`k^xQvmLSmq_=LZ>Z;r]OByMcUwch[sAWDZ;R:LJI<K^xuidyM<jI\\WPxkVQT:]tFVobH=DMCuYbaOl`YEAN:=:f\\Jf`YfvqIv>>;;CfkFJoYy_DosDUASEIWe;FdfmbH]ZLsuxAps\\Tsp`K<\\JB>BMR:]l>qPR]J;B>kDN;YqYi`ygiwUjIdfCc:Qx<Kf`Tk>es:dWKHletQbmLSMo_=LZ:KJJ>J=fS?rOwwVwYteSmwro_U<scD;cTGBy?gS;N^]vDyKRhbOQ`B><R::;W`;X_YIa?gSaWMeGqEU;CTm;uTCTm;RU]W^yXy[RPSU\\gvJ;F:=:BZRmDW^aWxAuPxSZMk:@oS<PEPm;Lu\\UN\\pv\\UM\\EQ><;J<BB[Wb;Fd@XMeQLQP<L^ZW_>gSUH<=b:JZ:>aJ?^CVmAN`s_f<vgE>KYu^uuyWcTGJ]\\JB:JJBj=NKUx:iSqAsM]J>ecm@oS>nSF^:?j::J:JYyo>mSF]JB\\qP<LotUUdy]iL\\pF@Z>>;:JJdPWHZD`Z>C:_DoSBnSF>;CJ:>BrYQBxYBpoC=CbkCBKUHjYDoSBn:^::JNDKBPm;\\nbH]mNb:@Z;:;;:<T^<NdmJJPn`gS:<B:Fj\\FZKW`:`\\oVZnB;<;F::J?M:;::J>:Zb:::<<:>N::J:;Z;<::@::b\\::ZB::K;::>>:Bb::Z:<:=>::F::J?;::K::\\<::BB:JJ;::;>:@B::R::ZD<::\\::>?::JJ:ZZ<::<B:FJ::j:::O>::>;:BD::ZZ::;?::>J:RZ::Z;::dB::B<:JN:::;;:<D::BZ:j:;::=::NK::J>:Zb:::<<:>N::J:;Z;<::@::b\\::ZB::K;::>>:Bb::Z:<:=>::F::J?;::K::\\<::BB:JJ;::;>:@B::R::ZD<::\\::>?::JJ:ZZ<::<B:FJ::j:::O>::>;:BD::ZZ::;?::>J:RZ::Z;::dB::B<:JN:::;;:<D::BZ:j:;::=::NK::J>:Zb:::<<:>N::J:;Z;<::@::b\\::ZB::K;::>>:Bb::Z:<:=>::F::J?;::K::\\<::BB:JJ;::;>:@B::R::ZD<::\\::>?::JJ:ZZ<::<B:FJ::j:::O>::>;:BD::ZZ::;?::>J:RZ::Z;::dB::B<:JN:::;;:<D::BZ:j:;::=::NK::J>:Zb:::<<:>N::J:;Z;<::@::b\\::ZB::K;::>>:Bb::Z:<:=>::F::J?;::K::\\<::BB:JJ;::;>:@B::R::ZD<::\\::>?::JJ:ZZ<::<B:FJ::j:::O>::>;:BD::ZZ::;?::>J:RZ::Z;::dB::B<:JN:::;;:<D::BZ:j:;::=::NK::J>:Zb:::<<:>N::J:;Z;<::@::b\\::ZB::K;::>>:Bb::Z:<:=>::F::J?;::K::\\<::BB:JJ;::;>:@B::R::ZD<::\\::>?::JJ:ZZ<::<B:FJ::j:::O>::>;:BD::ZZ::;?::>J:RZ::Z;::dB::B<:JN:::;;:<D::BZ:j:;::=::NK::J>:Zb:::<<:>N::J:;Z;<::@::b\\::ZB::K;::>>:Bb::Z:<:=>::F::J?;::K::\\<::BB:JJ;::;>:@B::R::ZD<::\\::>?::JJ:ZZ<::<B:FJ::j:::O>::>;:BD::ZZ::;?::>J:RZ::Z;::dB::B<:JN:::;;:<D::BZ:j:;::=::NK::J>:Zb:::<<:>N::J:;Z;<::@::b\\::ZB::K;::>>:Bb::Z:<:=>::F::J?;::K::\\<::BB:JJ;::;>:@B::R::ZD<::\\::>?::JJ:ZZ<::<B:FJ::j:::O>::>;:BD::ZZ::;?::>J:RZ::Z;::dB::B<:JN:::;;:<D::BZ:j:;::=::NK::J>:Zb:::<<:>N::J:;Z;<::@::b\\::ZB::K;::>>:Bb::Z:<:=>::F::J?;::K::\\<::BB:JJ;::;>:@B::R::ZD<::\\::>?::JJ:ZZ<::<B:FJ::j:::O>::>;:BD::ZZ::;?::>J:RZ::Z;::dB::B<:JN:::;;:<D::BZ:j:;::=::NK::J>:Zb:::<<:>N::J:;Z;<::@::b\\::ZB::K;::>>:Bb::Z:<:=>::F::J?;::K::\\<::BB:JJ;::;>:@B::R::ZDdcITmQSJ[xTwWYIEj;X@[e;sV:IEjmBV:::;wlmBDOU_ivqGDosisirKivQsboMIeos:WHZaCrSBHAbm;>::[gsmBhstBQfQkSEOeH[uTwBHqiRyDa=rS;@:::bdWHJ]tfsUxgcbGwIMWtyRWie;sV:ZV<::J_tVZiVG`OtEjbHw:qlV<udPmiiYvim[tV:?V:::Bwus:ETm_YsqH\\ofbGGdMI=ks:Zr:::JDms:YsTDUnQJKUt;hOs<pxqKDuuyXj\\uguvf:I=lC::JNem;Pn`;::k;::ZN<rn?gsYVwgTOytuAyu;CHAbmJV:::Ze_m;PnPGisig`xbGYSqDxEvOwUfSCisuLACJ;>\\::BnoDJcH=gwMcH=::<>Zb::<:BB:JJ[Z:B;J:;Z;<::@::b\\L>::\\::>?::JJ:ZZ<::<B:FJ::j:::O>::>;:BD::ZZ::;?::>J:RZ::Z;::dB::B<:JN:::;;:<D::BZ:j:;::=::NK::J>:Zb:::<<:>N::J:;Z;<::@::b\\::ZB::K;::>>:Bb::Z:<:=>::F::J?;::K::\\<::BB:JJ;::;>:@B::R::ZD<::\\::>?::JJ:ZZ<::<B:FJ::j:::O>::>;:BD::ZZ::;?::>J:RZ::Z;::dB::B<:JN:::;;:<D::BZ:j:;::=::NK::J>:Zb:::<<:>NRByg<qVrqX@ACJ;>Z:<JjET:]tv@KoYwEaRGALHA]>:;>:rZnvZ>nkOZ>:J<:JmeJ>WhwhiTF:\\:::VJ::B;:bs:J>::Z=<::C::GA:\\:::VJ::B;:bs:J>::Z=<::C::GA:\\:::VJ::B;:bs:J>::Z=<::C::GA:\\:::VJ::B;:bs:J>::Z=<::C::GA:\\:::VJ::B;:bs:J>::Z=<::C::GA:\\:::VJ::B;:bs:J>::Z=<::C::GA:\\:::VJ::B;:bs:J>::Z=<::C::GA:\\:::VJ::B;:bs:J>::Z=<::C::GA:\\:::VJ::B;:bs:J>::Z=tyABxCHyYwLSDKuF:;B:;RLEdMCde?DR?>:4:\"\{\}-%%ROOTG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YGF'-%-BOUNDS_WIDTHG6#$"%!4'F*-%.BOUNDS_HEIGHTG6#$"%!\$F*-%)CHILDRENG6%-%/TEXT_CONTAINERG6(-%/LINE_THICKNESSG6#$"#5F*-%(SPATIALG6&-%&TRANSG6#-%'VECTORG6$F(F(-%'ORIGING6#-%&POINTG6$$"%?AF*$"%];F*-%&SCALEG6#-FI6$F@F@-%)ROTATIONGF'-%,FIXED_WIDTHG6#%%trueG-%-FIXED_HEIGHTGFhn-%%DATAG6%7$$"%?7F*$"%S:F*7$$"%+?F*$"$?#F*%'CLOSEDG-%*PARAGRAPHG6#Qc\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6"-F;6(F=-FC6&FE-FL6#-FO6$$"%]dF*$"%]:F*FUFZFfnFjn-F]o6%7$$"%]ZF*$"%S9F*FdoFio-F[p6#Qc\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F^p-F;6(F=-FC6&FE-FL6#-FO6$$"%?SF*$"%I:F*FUFZFfnFjn-F]o6%7$$"%?IF*$"%?9F*FdoFio-F[p6#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F^pSo we can write :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(); # input placeholderJSFHand we know that 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Maple cannot read this type of equation, so we will write it again and at the end we will return to this form.
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(); # input placeholderHaving the two equations: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 so we can isolate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, knowing that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk=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(); # input 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(); # input placeholderNow we can derived LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21vR0YkNi1RKyZQYXJ0aWFsRDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRi1GIzYmLUYvNi1GMUYyL0Y2USZmYWxzZUYnL0Y5Rk4vRjtGTi9GPUZOL0Y/Rk4vRkFGTi9GQ0ZORkRGRy1GLzYtUSJ+RidGMkZNRk9GUEZRRlJGU0ZURkRGRy1JI21pR0YkNiVRImJGJy8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRidGMi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYG8vJSliZXZlbGxlZEdGTi1GWTYlUSJKRidGZm5GaW5GMg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EnYEpfX2JgRictSSNtb0dGJDYtUSomY29sb25lcTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRy1JJm1mcmFjR0YkNigtRjA2LVErJlBhcnRpYWxEO0YnRjMvRjdRJnVuc2V0RicvRjpGUS9GPEZRL0Y+RlEvRkBGUS9GQkZRL0ZERlEvRkZRJjAuMGVtRicvRklGWS1GIzYlLUYwNi1GT0YzRjZGOUY7Rj1GP0ZBRkNGWEZaLUYwNi1RIn5GJ0YzRjZGOUY7Rj1GP0ZBRkNGWEZaLUYsNiVRImJGJy8lJ2l0YWxpY0dRJXRydWVGJy9GNFEnaXRhbGljRicvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmlvLyUpYmV2ZWxsZWRHRjgtRiw2JVEkcmhzRidGX29GYm8tSShtZmVuY2VkR0YkNiQtRiM2Iy1GLDYlUSRlcTNGJ0Zfb0Zib0YzLUYwNi1RIj1GJ0YzRjZGOUY7Rj1GP0ZBRkNGRUZILUkjbW5HRiQ2JFEiMEYnRjM=print(); # input placeholderAnd knowing that 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(); # input 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(); # input placeholderprint(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnYXNzaWduRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2I1EhRictSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1FpZW0vSSJiRzYiKiYsNiomLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjIiIjIiIiSSV4X18xRzYiIiIjISIjKiYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMiIiMiIiJJJXhfXzJHNiIiIiMhIiMqJi1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyIiIyIiIkkleF9fbkc2IiIiIyEiIyomLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSV4X18xRzYiIiIiSSV4X18xRzYiIiIjIiIjKiYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJXhfXzJHNiIiIiJJJXhfXzJHNiIiIiMiIiMqJi1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kleF9fbkc2IiIiIkkleF9fbkc2IiIiIyIiIy1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyIiIyIjQy1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kleF9fMUc2IiEiKS1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kleF9fMkc2IiEiKS1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kleF9fbkc2IiEiKSIiIiwwKiRJJXhfXzFHNiIiIiUiIiMqJEkleF9fMkc2IiIiJSIiIyokSSV4X19uRzYiIiIlIiIjKiRJJXhfXzFHNiIiIiMhIzsqJEkleF9fMkc2IiIiIyEjOyokSSV4X19uRzYiIiIjISM7IiMnKiIiIiEiIkYnLyUrYWN0aW9udHlwZUdRPG1hcGxlc29mdC5jb206bGFiZWwoTDEyNjEyKUYnLyUldmlld0dRJmxhYmVsRidGOi9GM1Enbm9ybWFsRic=Now, let's return to series form,but instead of creating from this expression a series we can open the series that is given:First let look at the Denominator: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print(); # input placeholderNow let's take a look at the numerator: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEkTnVtRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEnZXhwYW5kRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNi0tRlM2JC1GIzYlLUklbXN1cEdGJDYlLUYsNiNRJ2B4X18xYEYnLUYjNiMtSSNtbkdGJDYkUSIyRidGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZoby1GXm82JFEiNEYnRjlGOS1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GYXAtRlM2JC1GIzYnLUYsNiVRJWNvc2hGJy9GMEY9RjktRlM2JC1GIzYjRmhuRjlGZG9GZ3AtRlM2JEZbb0Y5RjktRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSEZnb0Zpby1GUzYkLUYjNiUtRmZuNiUtRiw2I1EnYHhfXzJgRidGW29GYW9GZG9Gam9GOUZdcC1GUzYkLUYjNidGZ3AtRlM2JC1GIzYjRmpxRjlGZG9GZ3BGX3FGOUZhcS1GUzYkLUYjNiUtRmZuNiUtRiw2I1EnYHhfX25gRidGW29GYW9GZG9Gam9GOUZdcC1GUzYkLUYjNidGZ3AtRlM2JC1GIzYjRltzRjlGZG9GZ3BGX3FGOUY5Rl1wRl1vprint(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
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print(); # input placeholderAnd, has you can see, the expressions are the same!
JSFH
<Text-field style="Heading 1" layout="Heading 1">Q5</Text-field>Prove the connections 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 where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg== is a shear operator, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is a shift operator, and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5MTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy is a front differences operator.With the connections above find the coefficients LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiYkYnRi9GMkY1LUYsNiVRImNGJ0YvRjJGNS1GLDYlUSJkRidGL0YyRjk= in the derived formula: 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
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>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JSFHNote! Maple does not have all the operators you have learn, you need to build them! How to build them you can find in the Maple course notebook.Given the expression 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 we open the expression, we need to build the operators: (Because LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiREYnL0YwRj1GOUY5 are saved values in Maple we will call them LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiaUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEkZGlmRidGL0YyRjk=)forward differences operator: PkkmRGVsdGFHNiIsJi1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvSSJ4R0YkLCZGKyIiIkkiaEdGJEYtLUkiZkdGJDYjRitGLUYvISIiprint(); # input placeholderunit operator: PkkiaUc2Ii1JImZHRiQ2I0kieEdGJA==print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2L1EzJkRvdWJsZVJpZ2h0QXJyb3c7RicvJSVib2xkR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y0LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y5LyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjkvJShsYXJnZW9wR0Y5LyUubW92YWJsZWxpbWl0c0dGOS8lJ2FjY2VudEdGOS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkgvRjNRJ25vcm1hbEYnLCZJImlHNiIiIiJJJkRlbHRhR0YkRiU=print(); # input placeholderNow, let's find this expression series: LUkoY29udmVydEclKnByb3RlY3RlZEc2JC1JJ3Nlcmllc0dGJDYkLUkiZkc2IjYjLCZJInhHRisiIiJJImhHRitGL0YwSShwb2x5bm9tR0Ykprint(); # input placeholderderived operator: PkkkZGlmRzYiLUklZGlmZkclKnByb3RlY3RlZEc2JC1JImZHRiQ2I0kieEdGJEYsprint(); # input 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print(); # input placeholderThe first variable of the series is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yv which is equal to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkobWZlbmNlZEdGJDYkLUYjNiUtSSNtbkdGJDYkUSIwRicvRjZRJ25vcm1hbEYnRjJGNUZDRjJGNS8lMXN1cGVyc2NyaXB0c2hpZnRHRkItRjs2JC1GIzYkLUYvNiVRInhGJ0YyRjVGQ0ZDRkM=Shift operator: L0kiRUc2Ii1JJWV2YWxHJSpwcm90ZWN0ZWRHNiQtSSVzdWJzR0YnNiQvSSJ4R0YkLCYqJkkiaEdGJCIiIkkicEdGJEYxRjFGLUYxLUkiZkdGJDYjRi0vRjJGMQ==print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2L1EzJkRvdWJsZVJpZ2h0QXJyb3c7RicvJSVib2xkR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y0LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y5LyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjkvJShsYXJnZW9wR0Y5LyUubW92YWJsZWxpbWl0c0dGOS8lJ2FjY2VudEdGOS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkgvRjNRJ25vcm1hbEYnLUknc2VyaWVzRyUqcHJvdGVjdGVkRzYkLUklZXZhbEdGJDYkLUklc3Vic0dGJDYkL0kieEc2IiwmKiZJImhHRi4iIiJJInBHRi5GMkYyRi1GMi1JImZHRi42I0YtL0YzRjJGMQ==print(); # input placeholderLUkoY29udmVydEclKnByb3RlY3RlZEc2JCsxSSJoRzYiLUkiZkdGKDYjSSJ4R0YoIiIhLS1JIkRHNiRGJEkoX3N5c2xpYkdGKDYjRipGKyIiIiwkLS0tSSNAQEdGMTYkRjAiIiNGM0YrI0Y0RjtGOywkLS0tRjk2JEYwIiIkRjNGKyNGNCIiJ0ZCLCQtLS1GOTYkRjAiIiVGM0YrI0Y0IiNDRkosJC0tLUY5NiRGMCIiJkYzRisjRjQiJD8iRlItSSJPR0YkNiNGNEZESShwb2x5bm9tR0Ykprint(); # input placeholderAs we can see, the expressions are the same. therefore, 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, looking at the expression 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 we can say that: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print(); # input placeholder
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkbGhzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw== of the equationLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkcmhzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw== of the equationFrom the relation L0kiRUc2Ii1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjKiZJImhHRiQiIiJJJGRpZkdGJEYtprint(); # input placeholderJSFHwe know the series of LUkiZkc2IjYjLCYqJkkiaEdGJCIiIkkicEdGJEYpRilJInhHRiRGKQ==print(); # input placeholderThe series for this expression is:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=PkkjUzJHNiIqJiwsIiIiRicqJkkicEdGJEYnSSJSR0YkRidGJyoqRilGJywmRilGJyEiIkYnRidGKiIiIy1JKmZhY3RvcmlhbEclKnByb3RlY3RlZEc2I0YuRi1GJyosRilGJ0YsRicsJkYpRichIiNGJ0YnRioiIiQtRjA2I0Y2Ri1GJyouRilGJ0YsRidGNEYnLCZGKUYnISIkRidGJ0YqIiIlLUYwNiNGPEYtRidGJ0kiaUdGJEYnprint(); # input placeholderJSFHLUkoY29udmVydEclKnByb3RlY3RlZEc2JC1JKGlzb2xhdGVHNiI2JC9JIkVHRigtSSRleHBHNiRGJEkoX3N5c2xpYkdGKDYjKiZJImhHRigiIiItSSVkaWZmR0YkNiQtSSJmR0YoNiNJInhHRihGOkYzKiZGMkYzSSRkaWZHRihGM0kocG9seW5vbUdGJA==print(); # input placeholderJSFHon the same principle we can write the series for 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=And we know that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJpRidGL0YyLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GVi1GLDYlUScmIzkxNjtGJy9GMEY9RjlGOQ== so:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=PkkjUzFHNiIqJi1JKGNvbnZlcnRHJSpwcm90ZWN0ZWRHNiQtSSdzZXJpZXNHRig2JC1JI2xuRzYkRihJKF9zeXNsaWJHRiQ2IywmLkkmRGVsdGFHRiQiIiJGNUY1RjNJKHBvbHlub21HRihGNUkiaUdGJEY1print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=So, we can now build the equation:(We will write instead LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5MTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy , LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= )PkkkZXExRzYiLy1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvSSZEZWx0YUdGJEkiUkdGJEkjUzFHRiQqJi1GJzYkRipJI1MzR0YkIiIiLCoqJkYsIiIlSSJkR0YkRjJGMiomRiwiIiRJImNHRiRGMkYyKiZGLCIiI0kiYkdGJEYyRjIqJkYsRjJJImFHRiRGMkYyRjI=print(); # input placeholderPkkkZXEyRzYiLUknZXhwYW5kRyUqcHJvdGVjdGVkRzYjLUklc3Vic0dGJzYkLy1JImZHRiQ2I0kieEdGJCIiIkkkZXExR0Ykprint(); # input placeholderLy1JJGxoc0clKnByb3RlY3RlZEc2I0kkZXEyRzYiLUklc29ydEdGJTYjLUkkcmhzR0YlRiY=print(); # input placeholderWe get the next set of equations:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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JSFH
solving those equations we can find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiYkYnRi9GMkY1LUYsNiVRImNGJ0YvRjJGNS1GLDYlUSJkRidGL0YyRjk=:LUkmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDwmL0kmRGVsdGFHRicqJkkiYUdGJyIiIkYrRi4vLCQqJEYrIiIjIyEiIkYyKiYsJkkiYkdGJ0YuRi0hIiNGLkYrRjIvLCQqJEYrIiIkI0YuRjwqJkYrRjwsKEkiY0dGJ0YuRi1GPEY3RjhGLi8sJCokRisiIiUjRjRGRComRitGRCwqSSJkR0YnRi5GN0Y8RkBGOEYtISIlRi48JkYtRjdGQEZIprint(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=