1. (10 points) We want to approximate the function ln x for x = [1, e]...

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1. (10 points) We want to approximate the function ln x for x = [1, e] using a polynomial to the precision of 10-8. How should we choose the lowest degree polynomial to minimize the error over the interval? Justify your work theoretically, and write a Python program to plot your polynomial together with ln x over the interval [1, e], and another plot to show the error of approximation over the interval. Hint: dn dxn In x = (1)1 - (n 1)! xn 1. (10 points) We want to approximate the function ln x for x = [1, e] using a polynomial to the precision of 10-8. How should we choose the lowest degree polynomial to minimize the error over the interval? Justify your work theoretically, and write a Python program to plot your polynomial together with ln x over the interval [1, e], and another plot to show the error of approximation over the interval. Hint: dn dxn In x = (1)1 - (n 1)! xn

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To approximate the function lnx for x in 1 e using a polynomial to a precision of 108 and choose the lowest degree polynomial to minimize the error we ... View the full answer