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JSFHQuestionGiven two step functions, QyY+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkqcGllY2V3aXNlRyUqcHJvdGVjdGVkRzYmMjkkIiMlKiIiIjFGMkYxIiIhRiVGJUYlISIiPkkiZ0dGJWYqRidGJUYpRiUtRi02JkYwRjVGNEYzRiVGJUYlRjY=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=evidently both functions are discontinuous about the point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIzk0RidGOUY5 .LUkoZGlzY29udEc2IjYkLUkiZkdGJDYjSSJ4R0YkRik= = print(); # input placeholder , LUkoZGlzY29udEc2JSUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IkYmNiQtSSJnR0YnNiNJInhHRidGLA== = print(); # input placeholderThe sum of the functions, however should be a constant LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUSJ5RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEiPUYnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMUYnRj5GPkY+Rj4= inherently all over the domain, however Maple fails to notice the removal of the discontinuity:PkkiaEc2ImYqNiNJInhHRiRGJDYkSSlvcGVyYXRvckdGJEkmYXJyb3dHRiRGJCwmLUkiZkdGJDYjOSQiIiItSSJnR0YkRi5GMEYkRiRGJA==print(); # input placeholderLUkoZGlzY29udEc2JSUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IkYmNiQtSSJoR0YnNiNJInhHRidGLA==print(); # input placeholderWhy? What can be done?JSFHAnswerFirst, lets look under the hood and see what does Maple sees as the new function: LUkiaEc2IjYjSSJ4R0Ykprint(); # input placeholderWhen adding two complex expressions, sometimes Maple needs a little help or push in order to simplify them, the simplify and expand commands come handy at this stageLUkpc2ltcGxpZnlHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy1JImhHRic2I0kieEdGJw== = print(); # input placeholderand naturally now Maple is aware of the discontinuity removalLUkoZGlzY29udEc2JSUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IkYmNiQtSSlzaW1wbGlmeUc2JEYlRiY2Iy1JImhHRic2I0kieEdGJ0Yw = print(); # input placeholderJSFHJSFH