2x OO Suppose that Cnach (6 + ac) n=0 Find the first few coefficients. Co C1 C2 C3 = C4 Find the radius of convergence R of the power series. R2 32 (a) Evaluate the integral: dac 2 2+ 4 Your answer should be in the form k7, where k is an integer. What is the value of k? d 1 Hint: arctan (x) = dx x2 + 1 k (b) Now, let's evaluate the same integral using a power series. First, find the power series for the function 32 f (ac) = Then, integrate it from 0 to 2, and call the result S. S should be an infinite series. 202 + 4 What are the first few terms of S? ao a1 a2 a3 a4(c) The answers to part (a) and (b) are equal (why?). Hence, if you divide your infinite series from (b) by k (the answer to (a)), you have found an estimate for the value of 7 in terms of an infinite series. Approximate the value of 7 by the first 5 terms. (d) What is the upper bound for your error of your estimate if you use the first 11 terms? (Use the alternating series estimation.)