If $\mathrm{f}(x)=\frac{\sin \left(\pi \cos ^2 x\right)}{3 x^2}, x \neq 0$ is continuous at $x=0$ then $\mathrm{f}(0)=$

$$ \lim\limits_{x \rightarrow 5} \frac{\sqrt{2-2 \cos \left(x^2-12 x+35\right)}}{(x-5)}=\ldots \ldots $$

Let $\mathrm{A}=\mathop {\lim }\limits_{x \to {0^ + }}\left(1+\tan ^2 \sqrt{x}\right)^{\frac{1}{2 x}}$, then $\log _{\mathrm{e}} \mathrm{A}=$

The function $\mathrm{f}(x)=2 x-\left|x-x^2\right|$ is