$$\lim _\limits{x \rightarrow \infty} x^3\left\{\sqrt{x^2+\sqrt{1+x^4}}-x \sqrt{2}\right\}=$$

$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{1+x \sin x}-\sqrt{\cos x}}{\tan ^2 \frac{x}{2}}=$$

If $$f(x)$$ is continuous on its domain $$[-2,2]$$, where

$$f(x)=\left\{\begin{array}{cc} \frac{\sin a x}{x}+3 & , \text { for }-2 \leq x<0 \\ 2 x+7 & , \text { for } 0 \leq x \leq 1 \\ \sqrt{x^2+8}-b & , \text { for } 1< x \leq 2 \end{array}\right.$$ $$\text { then the value of } 2 a+3 b \text { is }$$

The function $$\mathrm{f}(\mathrm{t})=\frac{1}{\mathrm{t}^2+\mathrm{t}-2}$$ where $$\mathrm{t}=\frac{1}{x-1}$$ is discontinuous at