The series below converges to sin x for all x. Complete parts (a) through (c). sin x = x - x5 x x11 3! 5! 7! 9! 11! a. Find the first six terms of a series for cos x. For what values of x should the series converge? The first term of a series for cos x is. The second term of a series for cos x is. The third term of a series for cos x is The fourth term of a series for cos x is The fifth term of a series for cos x is. The sixth term of a series for cos x is. For what values of x should the series for cos x converge? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The series should converge for. (Type a compound inequality. Use integers or fractions for any numbers in the expression.) O B. The series should converge at x = . (Type an integer or a fraction.) O C. The series should converge for all values of x. b. By replacing x by 2x in the series for sin x, find a series that converges to sin 2x for all x. Choose the correct answer below. O A. sin 2x = 2- 22 x2 24 x 4 26 x 6 28 8 2! 21010 41 6! 81 10! + ... O B. sin 2x = x2 - - x 10 y 14 x 18 x21 10! 14 ! + 1 18! 211 + ... C. sin 2x = 2x - 25 x3 25 x5 2 x7 31 217 11 51 71 91 11! - + ... O D. sin 2x = 2x - 2x 2x5 2x' 2x 2x 11 31 51 71 91 1 1 1 + ... c. Using the result in part (a) and series multiplication, calculate the first six terms of a series for 2 sin x cos x. Compare your answer with the answer in part (b). O A. 2 sin x cos x = 2- 2*x 4 20x6 20 8 2 0 10 2! 4! 61 81 10! + ... O B. 2 sin x cos x = 2x - 2 x 2'X 3! 2 x11 5! 71 91 11! + ... O C. 2 sin x cos x = 2x - 2x 2x5 2x' 2xy 2x 11 31 51 71 91 111 + ... O D. 2 sin x cos x = 2x2 -. 2x6 2x 10 2x 14 2x 18 61 2x27 10! 141 181 21! Compare your answer with the answer in part (b). Choose the correct answer below. O A. The series for 2 sin x cos x is the same as the series for sin 2x. O B. The series for 2 sin x cos x is the series for sin 2x squared O C. The series for 2 sin x cos x is the series for sin 2x multiplied by x. O D. The series for 2 sin x cos x is twice the series for sin 2x