$$ f(x)= \begin{cases}{\left[x^2\right]-\left[-x^2\right],} & x \neq 3 \\ k & , x=3\end{cases} $$

is continuous at $x=3$, then $\mathrm{k}=$ where $[\cdot]$ is greatest integer function

$\mathop {\lim }\limits_{x \to 0} \frac{\left(7^x-1\right)^4}{\tan \left(\frac{x}{\mathrm{k}}\right) \cdot \log \left(1+\frac{x^2}{3}\right) \cdot \sin 4 x}=3(\log 7)^3$, then $\mathrm{k}=$

If $x^y+y^x=\mathrm{a}^{\mathrm{b}}$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}$ at $x=1, y=2$ is

The value of $\frac{(\cos \theta+i \sin \theta)^4}{(\sin \theta+i \cos \theta)^5}=$ where $\mathrm{i}=\sqrt{-1}$