Define $f(x)=\left\{\begin{array}{cl}b-a x & , \text { if } x<2 \\ 3 & , \text { if } x=2 \\ a+2 b x & , \text { if } x>2\end{array}\right.$ and if $\lim _{x \rightarrow 2} f(x)$ exists, then $\frac{a}{b}=$

The function $\mathrm{f}(x)=\sec \left[\log \left(x+\sqrt{1+x^2}\right)\right]$ is________function

The value of ${ }^{47} \mathrm{C}_4+\sum\limits_{\mathrm{j}=1}^5{ }^{(52-\mathrm{j})} \mathrm{C}_3$ is

Derivative of

$y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots \ldots \ldots \ldots \ldots \ldots \infty}}}$ is