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