$$ \mathop {\lim }\limits_{x \to \infty } \frac{3 x+4 \cos ^2 x}{\sqrt{x^2-5 \sin ^2 x}}= $$

If a function,

$$ f(x)=\left\{\begin{array}{cc} \frac{\sqrt[3]{1+a x^2+b x^3}-\sqrt[3]{1-a x^2-b x^3}}{x^2}, & x<0 \\ 5, & x=0 \\ \frac{\tan 3 x-\sin 3 x}{b x^3}, & x>0 \end{array}\right. $$

is continuous at $x=0$, then the geometric mean of $a$ and $b$ is

If $y=\log \left(\sec \left(\tan ^{-1} x\right)\right)(x>0)$, then $\frac{d y}{d x}$ at $x=1$ is

If $y=\sin ^{-1} \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}$ and $\frac{-3 \pi}{2}