1. Answer parts a through e using the function /(x) = In(1 + x) [8 pts] a. Find the eighth degree Taylor polynomial, centered at 0, to approximate (x) = In(1+ x) . Be sure to simplify your answer. b. Using your eighth degree polynomial from part a and Taylor's Inequality, If (x)SM for |x - al s d, then |E, (x) =[f(x)-P.(x)s M |x -to (n + D)! find the magnitude of the maximum possible error on [0. .1]. c. Approximate In(I.1) using your eighth degree Taylor polynomial. What is the actual error? Is it smaller than your estimated error? Round your answer to enough decimal places so you can determine. d. Create and submit a plot of the function along with your Taylor Polynomial. Based on your plot, what appears to be the interval of convergence? Explain