Using Taylor series, prove that +4 X (a) cos x = 1 - + —+... 2! 4! (b) sin x = x- +3 ts + 3! 5! +...

Which option below represents the Taylor series for the function x 0? about 1+ 2x4 a) 0 E-1)" - 2" xn+2 n=0 2(-1)--1 2x4+2 n! b) n=0 2" x 4n+2 (-1)". n! n=0

(2n)! Find a Maclaurin series for f(x). (Use for 1:3.5. (2n - 3).) --. 2"n!(2n-1) f(x) = 1 + f(x) = x + 16 n = 2

use Fourier sine series, consider f (x) = x² on [0, 7] to compute 1+1/22 + 1/32 + 1/4?... and take pi/4 = 1 - 1/3^3 + 1/5^5 ...