The approximate value of $(3.978)^{\frac{3}{2}}$ is

If $\mathrm{f}(x)=\left(\frac{1+\tan x}{1+\sin x}\right)^{\operatorname{cosec} x}$ is continuous at $x=0$ then $f(0)$ is equal to

$$\lim _\limits{x \rightarrow 0} \frac{9^x-4^x}{x\left(9^x+4^x\right)}=$$

The values of $a$ and $b$, so that the function

$$f(x)= \begin{cases}x+\mathrm{a} \sqrt{2} \sin x & , 0 \leq x \leq \frac{\pi}{4} \\ 2 x \cot x+b & , \frac{\pi}{4} \leq x \leq \frac{\pi}{2} \\ \mathrm{a} \cos 2 x-\mathrm{b} \sin x & , \frac{\pi}{2}< x \leq \pi\end{cases}$$

is continuous for $0 \leq x \leq \pi$, are respectively given by