Limit of $x[3-\cos(x^2)]$ using the epsilon-delta definition of a limit

Question

I have been asked to determine the limit $L$ of $x[3-\cos(x^2)]$ for $a=0$, and prove that it is the limit by showing how to find a $\delta$ such that $|f(x)-L|< \epsilon$, $\forall x$ satisfying $0<|x-a|<\delta$.

I understand that by definition $\delta=\min(1,...)$ and that $\delta$ depends on our $\epsilon$.

Thanks!