Question

How to apply the second part from the question in part (a)

Answer 1

\[\frac{-\frac{x^4}{2!} + \frac{x^8}{4!}-\ldots}{x^2} = -\frac{x^2}{2!} +\frac{x^6}{4!}- \ldots \]
\[\left[ -\frac{x^3}{3\cdot2!} + \frac{x^7}{7\cdot 6!}+\ldots \right]_0^1\]Something like this maybe?

Answer 2

@Ishaan94 are we apply -1 ??

Answer 3

take the maclaurin of cos(x^2) for a couple of terms and compare it to the expansion from the first

see if T(x^2), where T(x) is the expansion from the top, matches the cos(x^2) expansion