Directions: Write up the following: In this problem, we will investigate the Taylor series near :5 = 0 for f(:r) : .122 in (1 $21) A) Write out the first four non-zero terms of the Taylor series for f(:') = 332111 (1 7 gr) by nding using a known Taylor series. B) Find an expression for the general term of the Taylor series assuming that the starting value of the index is n = 1. C) Graph the function f (9:) and the Taylor polynomial found above on the same set of axes, and use this to approximate the radius of convergence of the Taylor series. Include a sketch of the graphs: With an explanation {in sentence form) of how you approximated the radius of convergence. D) Calculate the radius and interval of convergence using the ratio test. E) What is the value of f" (0)? fcllm)