If $f(x)= \begin{cases}\frac{8^x-4^x-2^x+1}{x^2}, & \text { if } x>0 \\ e^x \sin x+x+\lambda \log 4, & \text { if } x \leqslant 0\end{cases}$

is continuous at $x=0$ then the value of $1000 \mathrm{e}^\lambda=$

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

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 $\mathrm{f}(x)=\left\{\begin{array}{ll}\operatorname{m} x+1, & x \leqslant \frac{\pi}{2} \\ \sin x+\mathrm{n}, & x>\frac{\pi}{2}\end{array}\right.$, is continuous at $x=\frac{\pi}{2},(\mathrm{~m}, \mathrm{n} \in \mathbb{Z})$ then