Problem $1(10$ pts$)$: Evaluate the following limit using the Maclaurin series for $cos(x)$ :

$\underset{x0}{lim}\frac{1-cos(x^2)}{x^4}$

Hint: $cos(x)={\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^n}{(2n)!}{x}^{2n}$