+00 (-1)"2n (2n)! 1. For all x € R, cos a = n=0 (a) Find a power series that is equal to x cos(x2) for all a E R. (b) Differentiate the series in (la) to find a power series that is equal to cos(x2) –...

Extracted text: +00 (-1)"2n (2n)! 1. For all x € R, cos a = n=0 (a) Find a power series that is equal to x cos(x2) for all a E R. (b) Differentiate the series in (la) to find a power series that is equal to cos(x2) – 2x2 sin(x2) for all a eR. (c) Use the result in (1b) to prove that +oo (-16)" (4n + 1) (2n)! = cos(4) – 8 sin(4). n=0