Hi please help answer all parts of the attached question with as much explanation as possible so I can understand why you did what you did. Thank you!

Let f(x) = 111[(1 + x3)2]. a) Find the Maclaurin series for f (x). What is its radius of convergence? You may make use of any standard Maclaurin series and their properties, provided you state them clearly. b) Show that the derivatives of f satisfy f (3\"+1)(0) = f 6\"\" (0) = 0 for all integers n 2 0. Find and state a formula for f (3")(0) valid for n21. G) Let I = f (x) dx. 0 i) Using the MacLaurin series for f , write I as a series. ii) Let I 3 be the approximation to I obtained from just the first three nonzero terms in the series. Without computing I or I3, use the Alternating Series Estimation Theorem to find R such that |I I3|