EXERCISE 20 (AP Calculus BC - Exam 2017, MC.29) (No calculator) Which of the following is a power series expansion of e te-* 2 A) 1+ x 2n 2! 4! 6! + ...+ (2n)! it ... B) 1- 2! 4! 6! + ... + ( -1) "_x2n It ... (2n)! C) att x x x 2 n+1 3! 5! 7! + ...+- (2n +1)! + ... D) x- x x x 3! 5! 7! TT + ... + ( - 1)" x 2 n+1 (2n+ 1 ) ! + ... EXERCISE 21 (Cliffs AP Calculus AB and BC, 3rd Edition, Chapter 8B, MC.3) A power series for sin(x2 ) could be A) 1- 21 4! 6! + ... D) X 14 81 3! 5! 7! 9 ! -+ ... B) x2 _ x x10 - 14 18 5 7 9 E) 1+x2 - x x x8 2! 3! 4 ! - + ... 10 x 2 . x 14 1 18 C) 3 ! 5 ! 7! 9! + ... EXERCISE 22 (Cliffs AP Calculus AB and BC, 3rd Edition, Chapter 8B, FR.1) Suppose P(x) = -3 + 5(x -2) - 7(x - 2)2 + 6(x-2)3 is the third-degree Taylor polynomial for the function g about 2. Assume that g is differentiable for all orders for all real numbers. a) Find g (2). b) Find g"(2). c) Write the fourth-degree Taylor polynomial for h, given that h(x) = Jig(:) di . d) Write the second-degree Taylor polynomial for g' about 2. e) Use the result of part (d) to estimate g'(2. 1)