Let $\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$ is differentiable function having $\mathrm{f}(3)=3, \mathrm{f}^{\prime}(3)=\frac{1}{27}$ and $\mathrm{g}(x)= \begin{cases}\int_3^{\mathrm{f}(x)} \frac{3 \mathrm{t}^2}{x-3} \mathrm{dt}, & \text { if } x \neq 3 \\ \mathrm{~K}, & \text { if } x=3\end{cases}$ is continuous at $x=3$, then $\mathrm{K}=$

If Rolle's theorem holds for the function $x^3+\mathrm{a} x^2+\mathrm{b} x, 1 \leq x \leq 2$ at the point $\frac{4}{3}$, then the values of $a$ and $b$ are respectively

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

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