Hope someone can help me.

Qn 1 : Is the function $\displaystyle f(x)=\sqrt[3]{e^x-1-x-\frac{x^2}{2}}$ differentiable at $\displaystyle x=0$

Qn 2 : Compute the limit $\displaystyle \lim_{n \to \infty}\int_{0}^{\pi}cos(x^n)\, dx$.

Thanks in advance.