Consider the function f(x) = sin (x7). a. Differentiate the Taylor series alfout 0 for f(x). b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Choose the correct answer below. 7x20 7x34 2! 4! OA. 7x-. OC. -7x13. + 7x27 3! 5! 7x48 6! О в. 7x6 OD. -7x' 7x20 2! b. f'(x) = c. The interval of convergence of the power series for the derivative is (Simplify your answer. Type an inequality or a compound inequality. Type an expression using x as the variable.) + 13 7x²7 3! 7x34 4! 41 7x" 5! 7x48 6! + ...

a. Differentiate the Taylor series about 0 for the function f(x) = ²x b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Which of the following is the derivative of the Taylor series about x = 0? O A. ∞0 k=1 Ο c. 2 Σ #3 (2)kxk-1 (k-1)! 00 xk-1 (k-1)! k=0 b. What is the function represented by the differentiated series? f(x) = 0 c. What is the interval of convergence? C S4 $ 45 % MacBook Pro Search or type URL ^ 6 & 7 ... 00 Ο Β. Σ k=0 ∞ xk OD. 2 Σ (k-1)! k=1 * xk-1 (k-1)! 8 This que 9

-1 72. Find ƒ(7) (0) and ƒ(8) (0) for ƒ(x) = tan series. x using the Maclaurin

Find the first four nonzero terms in the Maclaurin series for the function. f(x)=x sin(4x) 32 OA. 4x²+. OB. 4x-8x3 OC. 4x- 32 + OD. 4x2. 32 +4 + 2-32x + 128 15 512 15 + 128 15 1024 + -x8 315 4096 45 -x6 -x7 4096 315 +8 1024 -x8 315 ... Time Remaining.