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<Text-field style="Heading 1" layout="Heading 1">Q1</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5In the following drawing cylindrical water tank is displayed. The tank is filled from above and water running out through the hose attached to it's bottom. The rate of change in water level, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2ZvcmVncm91bmRHUSpbMTI4LDAsMF1GJy8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJy9GM1Enbm9ybWFsRic=, is described by the following differential equation: 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The following data belong to a certain water tank 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, using a computer, the water level as a function of time until 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 Where at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5LyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0Y5 we know 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=There are two methods to solve the following: Euler method and the RonghKotta fourth order method, and compare the results. Draw the resultsLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 3" layout="Heading 3">Theoretical</Text-field>Writing the expression in more simple form: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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 4" layout="Heading 4"><Font bold="true">Euler</Font></Text-field>We know that Euler method is: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEmRXVsZXJGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYjUSlgSF9fbisxYEYnLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUYsNiNRJ2BIX19uYEYnLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GZm4tRiw2JVEiaEYnRi9GMi1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GX28tRiw2JVEiZkYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiNRJ2B0X19uYEYnLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGXm8vRk5RLDAuMzMzMzMzM2VtRidGVUY5print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 4" bold="true" layout="Heading 4"><Font bold="true">RungeKutta </Font><Equation executable="false" style="Heading 4" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1cEdGJDYlLUkjbW5HRiQ2J1EiNEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2Ji1JI21pR0YkNiZRI3RoRidGMi9GOVEsYm9sZC1pdGFsaWNGJ0Y7RjJGQ0Y7LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnRjJGNUY4Rjs=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1cEdGJDYlLUkjbW5HRiQ2J1EiNEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2Ji1JI21pR0YkNiZRI3RoRidGMi9GOVEsYm9sZC1pdGFsaWNGJ0Y7RjJGQ0Y7LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnRjJGNUY4Rjs=</Equation><Font bold="true"> order</Font></Text-field>We know that RungeKutta LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbW5HRiQ2JFEiNEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbWlHRiQ2JVEjdGhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRidGO0Y+LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GODYjUSFGJ0Yy order method is: 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print(); # input placeholderWhere, 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print(); # input placeholderSo, in our case, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 3" layout="Heading 3">Programming</Text-field>
<Text-field style="Heading 4" layout="Heading 4"><Font bold="true">Euler Method</Font></Text-field>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A__tank := 3.13:
A__pipe := 0.6e-2:
K__2 := 200:
K__1 := 300:
rho := 1000:
g := 9.81:
t := 0:
H[1] := 3:
h := 0.1e-1:
n := 1:
while H[n] >= 10^(-4) do
t := h*n:
H[n+1] := evalf(H[n]-h*(K__1+K__2*cos((1/12)*Pi*t)-rho*A__pipe*sqrt(2*g*H[n]))/(rho*A__tank)):
Euler[n] := H[n]:
Time[n] := t:
n := n+1:
end do:
Euler := `<,>`(seq(Euler[j], j = 1 .. n-1)):
Time := `<,>`(seq(Time[j], j = 1 .. n-1)):
plot(Time, Euler, title = "Hight Vs. Time", labels = ["Time [Sec] ", "Hight[m]"],
labeldirections = ["horizontal", "vertical"],color=red,gridlines);LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 4" layout="Heading 4"><Font bold="true">RungeKutta </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1cEdGJDYlLUkjbW5HRiQ2JlEiNEYnLyUlYm9sZEdRJXRydWVGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNy1GIzYpLUkjbWlHRiQ2J1EjdGhGJ0YyLyUnaXRhbGljR0Y0L0Y2USxib2xkLWl0YWxpY0YnRjgvJSdmYW1pbHlHUS9UaW1lc35OZXd+Um9tYUYnRjJGQC8lMGZvbnRfc3R5bGVfbmFtZUdRKkhlYWRpbmd+NEYnRkJGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGMkZHRjVGOA==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1cEdGJDYlLUkjbW5HRiQ2JlEiNEYnLyUlYm9sZEdRJXRydWVGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNy1GIzYpLUkjbWlHRiQ2J1EjdGhGJ0YyLyUnaXRhbGljR0Y0L0Y2USxib2xkLWl0YWxpY0YnRjgvJSdmYW1pbHlHUS9UaW1lc35OZXd+Um9tYUYnRjJGQC8lMGZvbnRfc3R5bGVfbmFtZUdRKkhlYWRpbmd+NEYnRkJGOC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGMkZHRjVGOA==</Equation><Font bold="true"> order Method</Font></Text-field>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JSFHJSFHJSFHA__tank := 3.13:
A__pipe := 0.6e-2:
K__2 := 200:
K__1 := 300:
rho := 1000:
g := 9.81:
H[1] := 3:
h := 0.1e-1:
k := 1:
while H[k] >= 10^(-4) do
t := h*k:
b__1 := h*evalf(eval((K__1+K__2*cos((1/12)*Pi*T)-rho*A__pipe*sqrt(2*g*Hight))/(rho*A__tank), {Hight = H[k], T = t})):
b__2 := h*evalf(eval((K__1+K__2*cos((1/12)*Pi*T)-rho*A__pipe*sqrt(2*g*Hight))/(rho*A__tank), {Hight = H[k]+(1/2)*b__1, T = t+(1/2)*h})):
b__3 := h*evalf(eval((K__1+K__2*cos((1/12)*Pi*T)-rho*A__pipe*sqrt(2*g*Hight))/(rho*A__tank), {Hight = H[k]+(1/2)*b__2, T = t+(1/2)*h})):
b__4 := h*evalf(eval((K__1+K__2*cos((1/12)*Pi*T)-rho*A__pipe*sqrt(2*g*Hight))/(rho*A__tank), {Hight = H[k]+b__3, T = t+h})):
H[k+1] := evalf(H[k]-1/6*(b__1+2*b__2+2*b__3+b__4)):
RungeKutta[k] := H[k]:
Time[k] := t:
k := k+1:
end do:
RungeKutta := `<,>`(seq(RungeKutta[j], j = 1 .. k-1)):
Time := `<,>`(seq(Time[j], j = 1 .. k-1)):
plot(Time, RungeKutta, color=red, gridlines,title = "Hight Vs. Time", labels = ["Time [Sec] ", "Hight[m]"],
labeldirections = ["horizontal", "vertical"]);
JSFHJSFHJSFH
<Text-field style="Heading 1" layout="Heading 1">Q2</Text-field>Using Simpson method to calculate the integral 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 numerically, Prove that the use of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRJDAuMUYnRjlGOQ== interval ensure us overall error that is less than 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkobXN1YnN1cEdGJDYnLUY2Ni9RJiZpbnQ7RicvJStmb3JlZ3JvdW5kR1EuWzE0NCwxNDQsMTQ0XUYnRjkvSSttc2VtYW50aWNzR0YkUSZpbmVydEYnRjtGPi9GQUYxRkIvRkVGMUZGRkgvRktRJjAuMGVtRicvRk5GaG4tRiM2Iy1JI21uR0YkNiRRIjBGJ0Y5LUYjNiMtRl1vNiRRIjFGJ0Y5LyUxc3VwZXJzY3JpcHRzaGlmdEdGX28vJS9zdWJzY3JpcHRzaGlmdEdGX28tRiw2JVEieEYnRi9GMi1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkhGZ25GaW4tSSVtc3VwR0YkNiUtRjY2LVEvJkV4cG9uZW50aWFsRTtGJ0Y5RjtGPkZARkJGREZGRkhGZ24vRk5RLDAuMTExMTExMWVtRictRiM2JS1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRmduRmluLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZgcUZpb0Zlb0ZpcC1GNjYvUTAmRGlmZmVyZW50aWFsRDtGJ0ZVRjlGWEY7Rj5GQEZCRkRGRkZIRmduRmluRmlvLUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEtR2V0SW50ZWdyYW5kRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiMtRiw2JVEiVEYnRi9GMi9GM1Enbm9ybWFsRictRiw2I1EhRic=print(); # input placeholderWe can see that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input placeholderUsing Simpson method: 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print(); # input placeholderAs we can see, the upper limit of the integral :LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEiMUYnRjktRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0= ,the lower limit of the integral print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEiMEYnRjktRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0= and, the interval, print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkjbW5HRiQ2JFEkMC4xRidGOS1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRkpGTQ==print(); # input placeholderWe know that the error is: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=print(); # input 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYjUSFGJy1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUWpvMi1JJGFic0clKnByb3RlY3RlZEc2I0kiUkc2IiwkLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMhIiIkIis2NjY2NiEjOkYnLyUrYWN0aW9udHlwZUdROm1hcGxlc29mdC5jb206bGFiZWwoTDIwMClGJy8lJXZpZXdHUSZsYWJlbEYnRjovRjNRJ25vcm1hbEYnprint(); # input placeholder
We got that the error R<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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
JSFH
<Text-field style="Heading 1" layout="Heading 1">Q3</Text-field>Given differential equation 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 With initial conditions LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMEYnL0YzUSdub3JtYWxGJ0Y+Rj4tSSNtb0dGJDYtUSI9RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZVLUY7NiRRIjFGJ0Y+Rj4=Also given the following numeric method: 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Where 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 And LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5 integration step And LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEiYkYnRi9GMi1GNjYtUSJ+RidGOUY7L0Y/Rj1GQEZCRkRGRkZIRkovRk5GTEY5are real, given, positive constants.Find the local accuracy of the given method.JSFH
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>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print(); # input 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print(); # input 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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Let write the series of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNiVRIm5GJ0YyRjUtSSNtb0dGJDYtUSIrRicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlQtSSNtbkdGJDYkUSIxRidGQUYyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZB: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(); # input 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print(); # input placeholderSo... 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print(); # input placeholderAnd.... 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print(); # input placeholderPlacing the series we found in the original expression above, we get:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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print(); # input placeholderJSFHJSFHJSFHComparing coefficients:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYHlfX25gRictSSNtb0dGJDYtUSI6RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRjA2LVEifkYnRjNGNkY5RjtGPUY/RkFGQy9GRlEmMC4wZW1GJy9GSUZORjM=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlRi4vRjBGPUY5Rjk=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EnYHlfX25gRictSSNtb0dGJDYtUSInRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnRi8tRjA2LVEiOkYnRjNGNkY5RjtGPUY/RkFGQy9GRlEsMC4yNzc3Nzc4ZW1GJy9GSUZPRjM=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print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EnYHlfX25gRictSSNtb0dGJDYtUSInRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnRi9GL0YvLUYwNi1RIjpGJ0YzRjZGOUY7Rj1GP0ZBRkMvRkZRLDAuMjc3Nzc3OGVtRicvRklGT0YzLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEmc29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GNjYmLUYjNiotSSZtZnJhY0dGJDYoLUklbXN1cEdGJDYlLUYsNiVRImhGJ0YvRjItRiM2Iy1JI21uR0YkNiRRIjRGJy9GM1Enbm9ybWFsRicvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYjNiMtRko2JFEjMjRGJ0ZNLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zmbi8lKWJldmVsbGVkR1EmZmFsc2VGJy1JI21vR0YkNi1RIj1GJ0ZNLyUmZmVuY2VHRltvLyUqc2VwYXJhdG9yR0Zbby8lKXN0cmV0Y2h5R0Zbby8lKnN5bW1ldHJpY0dGW28vJShsYXJnZW9wR0Zbby8lLm1vdmFibGVsaW1pdHNHRltvLyUnYWNjZW50R0Zbby8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmBwLUY2NiQtRiM2JS1GLDYjUSFGJy1GIzYoLUZdbzYtUSomdW1pbnVzMDtGJ0ZNRmBvRmJvRmRvRmZvRmhvRmpvRlxwL0ZfcFEsMC4yMjIyMjIyZW1GJy9GYnBGYHEtRiM2JS1GPzYoLUZKNiRGWUZNLUZKNiRRIjhGJ0ZNRldGWkZnbkZpbi1GXW82LVExJkludmlzaWJsZVRpbWVzO0YnRk1GYG9GYm9GZG9GZm9GaG9Gam9GXHAvRl9wUSYwLjBlbUYnL0ZicEZfci1GIzYlLUZCNiVGREZJRk9GW3ItRiw2JVEiYkYnRi9GMi1GXW82LVEnJnBsdXM7RidGTUZgb0Zib0Zkb0Zmb0Zob0Zqb0ZccEZfcUZhcS1GIzYlLUY/NihGZnEtRko2JFEjMTJGJ0ZNRldGWkZnbkZpbkZbckZjci1GXW82LVEoJm1pbnVzO0YnRk1GYG9GYm9GZG9GZm9GaG9Gam9GXHBGX3FGYXEtRiM2JS1GPzYoRmZxRlRGV0ZaRmduRmluRltyLUYjNiUtRiw2JVEiYUYnRi9GMkZbckZjckZncEZNLUZdbzYtUSIsRidGTUZgby9GY29GMUZkb0Zmb0Zob0Zqb0ZccEZeci9GYnBRLDAuMzMzMzMzM2VtRidGZXJGXG8tSShtYWN0aW9uR0YkNiUtSSptdmVyYmF0aW1HRiQ2I1EoIyIiIiIiJEYnLyUrYWN0aW9udHlwZUdRO21hcGxlc29mdC5jb206bGFiZWwoTDE3NjQpRicvJSV2aWV3R1EmbGFiZWxGJ0ZncEZNLyUlb3BlbkdRInxmckYnLyUmY2xvc2VHUSJ8aHJGJ0ZedC1GNjYmLUYjNiVGW3RGXnRGZXJGTUZhdUZkdUZNprint(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EnYHlfX25gRictSSNtb0dGJDYtUSInRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnRi9GL0YvRi8tRjA2LVEiOkYnRjNGNkY5RjtGPUY/RkFGQy9GRlEsMC4yNzc3Nzc4ZW1GJy9GSUZPRjM=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print(); # input placeholderJSFH
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=JSFH
<Text-field style="Heading 1" layout="Heading 1">Q4</Text-field>Art 1: Prove the connection 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 where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMg=== Operator of differentiation. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic== Spacing between close points. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDg7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy= Operator of the central differencesLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Art 2: Given the integral 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 Using the connection of the previous Article, show that the integral can be expressed by the operator of the central differences according to: 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 are the values \342\200\213\342\200\213LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EnYGFfXzBgRictSSNtb0dGJDYtUSIsRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiNRJ2BhX18xYEYnRi8tRiw2I1EnYGFfXzJgRidGMw==?(Note! You allowed to use the next series: 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 = print(); # input placeholder)
<Text-field style="Heading 2" layout="Heading 2">Solution</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field style="Heading 3" layout="Heading 3">Art 1</Text-field>LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZULyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZQNiZGUkZVRlgvRmVuUSVhdXRvRictRiw2JVEqaW50ZXJmYWNlRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEsdHlwZXNldHRpbmdGJ0YvRjItRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRiw2JVEpZXh0ZW5kZWRGJ0YvRjJGOUY1LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEjaERGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSSNtbkdGJDYkUSIyRidGOS1GNjYtUScmc2RvdDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRJjAuMGVtRicvRk5GVy1JJW1zdXBHRiQ2JS1GLDYlUSVzaW5oRicvRjBGPUY5LUYjNiYtRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmBvLUZQNiRRIjFGJ0Y5Ri9GMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1JJm1mcmFjR0YkNigtRiw2JVEnJiM5NDg7RidGaW5GOS1GIzYlRk9GL0YyLyUubGluZXRoaWNrbmVzc0dGZG8vJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGaXAvJSliZXZlbGxlZEdGPUY5RjktRjY2L1EzJkRvdWJsZVJpZ2h0QXJyb3c7RicvJSVib2xkR0YxL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0ZkcUY7Rj4vRkFGMUZCRkRGRkZIRkpGTUY5LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkmbWZyYWNHRiQ2KC1JI21pR0YkNiVRI2hERicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIyRicvRjZRJ25vcm1hbEYnRjJGNS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRS8lKWJldmVsbGVkR1EmZmFsc2VGJy1JI21vR0YkNi1RIj1GJ0Y+LyUmZmVuY2VHRkovJSpzZXBhcmF0b3JHRkovJSlzdHJldGNoeUdGSi8lKnN5bW1ldHJpY0dGSi8lKGxhcmdlb3BHRkovJS5tb3ZhYmxlbGltaXRzR0ZKLyUnYWNjZW50R0ZKLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGaW4tSSVtc3VwR0YkNiUtRi82JVElc2luaEYnL0YzRkpGPi1GIzYmLUZMNi1RKiZ1bWludXMwO0YnRj5GT0ZRRlNGVUZXRllGZW4vRmhuUSwwLjIyMjIyMjJlbUYnL0Zbb0Zpby1GOzYkRkJGPkYyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2KC1GLzYlUScmIzk0ODtGJ0Zib0Y+RjhGQEZDRkZGSEY+Rj4tRkw2L1EzJkRvdWJsZVJpZ2h0QXJyb3c7RicvJSVib2xkR0Y0L0Y2USVib2xkRicvJStmb250d2VpZ2h0R0ZgcUZPRlEvRlRGNEZVRldGWUZlbkZnbkZqbkY+LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVElc2luaEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2JC1JJm1mcmFjR0YkNigtRiw2JVEjaERGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnRjJGQEZCLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZPLyUpYmV2ZWxsZWRHRjFGMkYyLUkjbW9HRiQ2LVEiPUYnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Ziby1GOzYoLUYsNiVRJyYjOTQ4O0YnRi9GMkZERkpGTUZQRlJGMg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictRiM2KS1GLDYlUSgmZGVsdGE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnRjcvJSZmZW5jZUdGNi8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y2LyUobGFyZ2VvcEdGNi8lLm1vdmFibGVsaW1pdHNHRjYvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZOLUYsNiVRJXN1YnNGJy9GNVEldHJ1ZUYnL0Y4USdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYrLUYsNiVRInhGJ0ZURlYtRjs2LVEiPUYnRjdGPkZARkJGREZGRkhGSkZMRk9GZ24tRjs2LVEiK0YnRjdGPkZARkJGREZGRkhGSi9GTVEsMC4yMjIyMjIyZW1GJy9GUEZhby1JJm1mcmFjR0YkNigtRiw2JVEiaEYnRlRGVi1GIzYjLUkjbW5HRiQ2JFEiMkYnRjcvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmRwLyUpYmV2ZWxsZWRHRjYtRjs2LVEifkYnRjdGPkZARkJGREZGRkhGSi9GTVEmMC4wZW1GJy9GUEZdcS1GOzYtUSIsRidGN0Y+L0ZBRlVGQkZERkZGSEZKRlxxL0ZQUSwwLjMzMzMzMzNlbUYnLUYsNiVRImZGJ0ZURlYtRlk2JC1GIzYjRmduRjdGNy1GOzYtUSgmbWludXM7RidGN0Y+RkBGQkZERkZGSEZKRmBvRmJvRlEtRlk2JC1GIzYrRmduRmpuRmduLUY7Ni1RKiZ1bWludXMwO0YnRjdGPkZARkJGREZGRkhGSkZgb0Zib0Zjb0ZpcEZfcUZlcUZocUY3Ris=print(); # input 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(); # input placeholder= 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 can see that the series above is the taylor series for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1cEdGJDYlLUkjbW9HRiQ2LVEvJkV4cG9uZW50aWFsRTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMTExMTExMWVtRictRiM2Jy1JJm1mcmFjR0YkNigtSSNtaUdGJDYlUSNoZEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YzUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnRjJGU0ZWLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zdby8lKWJldmVsbGVkR0Y3RlMvJStmb3JlZ3JvdW5kR1EsWzEyOCwwLDEyOF1GJy8lLHBsYWNlaG9sZGVyR0ZVRlYvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYvNi1RJyZzZG90O0YnRjJGNUY4RjpGPEY+RkBGQkZEL0ZIRkYtRlA2JVEiZkYnRlNGVi1JKG1mZW5jZWRHRiQ2JC1GIzYkLUZQNiVRInhGJ0ZTRlZGMkYyRjI=Therefore, 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So, 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 = print(); # input placeholderJSFHJSFHJSFH
<Text-field style="Heading 3" layout="Heading 3">Art 2</Text-field>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(); # input placeholderPkkkZXEyRzYiLy1JJHJoc0clKnByb3RlY3RlZEc2I0kkZXExR0YkLUkkaW50R0YkNiQtSSJ5R0YkNiNJInRHRiQvRjE7LCZJJXhfXzBHRiQiIiJJImhHRiQjISIiIiIjLCZGNUY2RjcjRjZGOg==print(); # input placeholderLyomSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIiLUkkbGhzR0YmNiNJJGVxMkdGKEYpKiZGJEYpLUkkcmhzR0YmRixGKQ==print(); # input placeholderLy1JJHJoc0clKnByb3RlY3RlZEc2Iy8qKEkiREc2JEYlSShfc3lzbGliRzYiIiIiSSJoR0YsRi0sKCooSSVhX18yR0YsRi1JJmRlbHRhR0YsIiIlSSV5X18wR0YsRi1GLSooSSVhX18xR0YsRi1GMiIiI0Y0Ri1GLSomSSVhX18wR0YsRi1GNEYtRi1GLSomRilGLS1JJGludEdGKjYkLUkieUdGLDYjSSJ0R0YsL0ZBOywmSSV4X18wR0YsRi1GLiMhIiJGNywmRkVGLUYuI0YtRjdGLSwmLUkiZkdGLDYjRkhGLS1GTDYjRkRGRw==print(); # input placeholder\342\207\222 PkkkZXEzRzYiLy1JJGxoc0clKnByb3RlY3RlZEc2Iy8qJkkiREc2JEYoSShfc3lzbGliR0YkIiIiLUkkaW50R0YtNiQtSSJ5R0YkNiNJInRHRiQvRjY7LCZJJXhfXzBHRiRGL0kiaEdGJCMhIiIiIiMsJkY6Ri9GOyNGL0Y+Ri8sJi1JImZHRiQ2I0Y/Ri8tRkM2I0Y5Rj1JJmRlbHRhR0Ykprint(); # input placeholderhence, LyomSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIiLUkkbGhzR0YmNiNJJGVxMkdGKEYpLUkkcmhzR0YmNiNJJGVxM0dGKA==print(); # input placeholderUsing the identity from previous article, PkkkZXE0RzYiLywkKiYtSShhcmNzaW5oR0YkNiMsJEkmZGVsdGFHRiQjIiIiIiIjRi4sKCooSSVhX18yR0YkRi5GLCIiJUkleV9fMEdGJEYuRi4qKEklYV9fMUdGJEYuRixGL0Y0Ri5GLiomSSVhX18wR0YkRi5GNEYuRi5GLkYvRiw=print(); # input placeholderthe series of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoYXJjc2luaEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2Ji1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRidGMi1GIzYlLUY+NiRRIjJGJ0YyL0YwUSV0cnVlRicvRjNRJ2l0YWxpY0YnLyUubGluZXRoaWNrbmVzc0dGQC8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZOLyUpYmV2ZWxsZWRHRjEtSSNtb0dGJDYtUScmc2RvdDtGJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGYW8tRiw2JVEnJiM5NDg7RidGL0YyRjJGMkYy is:LUknc2VyaWVzRyUqcHJvdGVjdGVkRzYkLUkoYXJjc2luaEc2JEYkSShfc3lzbGliRzYiNiMsJEkmZGVsdGFHRiojIiIiIiIjRi0=print(); # input placeholderSo, PkkkZXE1RzYiLywkKiYtSShjb252ZXJ0RyUqcHJvdGVjdGVkRzYkLUknc2VyaWVzR0YqNiQtSShhcmNzaW5oRzYkRipJKF9zeXNsaWJHRiQ2IywkSSZkZWx0YUdGJCMiIiIiIiNGNUkocG9seW5vbUdGKkY3LCgqKEklYV9fMkdGJEY3RjUiIiVJJXlfXzBHRiRGN0Y3KihJJWFfXzFHRiRGN0Y1RjhGPkY3RjcqJkklYV9fMEdGJEY3Rj5GN0Y3RjdGOEY1print(); # input placeholderLUklc29ydEclKnByb3RlY3RlZEc2JS1JKGNvbGxlY3RHNiRGJEkoX3N5c2xpYkc2IjYkLUknZXhwYW5kR0YkNiNJJGVxNUdGKjcnSSZkZWx0YUdGKiokRjEiIiQqJEYxIiImKiRGMSIiKCokRjEiIipGMUkqYXNjZW5kaW5nR0Yqprint(); # input placeholderComparing coefficients: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
We got 3 equations with 3 variables:LUkmc29sdmVHNiI2JDwlLyomSSZkZWx0YUdGJCIiIkklYV9fMEdGJEYqRikvLCYqJkklYV9fMUdGJEYqRikiIiRGKiomRilGMEYrRiojISIiIiNDIiIhLywoKiZJJWFfXzJHRiRGKkYpIiImRioqJkYvRipGKUY6RjIqJkYpRjpGK0YqI0YwIiRTJ0Y1PCVGK0YvRjk=print(); # input placeholderLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=