The function $f:R\to R$ defined by $f\left(x\right)=\underset{n\to \infty }{\lim }\frac{\cos \left(2\pi x\right)-x^{2n}\sin \left(x-1\right)}{1+x^{2n+1}-x^{2n}}$ is continuous for all $x$ in

Let the function $f\left(x\right)=\left\{\begin{array}{cc}\frac{{\log }_e\left(1+5x\right)-{\log }_e\left(1+\alpha x\right)}{x}& \mathrm{if} x\ne 0\\ 10& \mathrm{if} x=0\end{array}\right.$ be continuous at $x=0$. Then $\alpha$ is equal to

If the function $f\left(x\right)=\left\{\begin{array}{cc}\left(1+|\cos x|\right)\frac{\lambda }{|\cos x|},& 0<x<\frac{\pi }{2}\\ \mu ,& x=\frac{\pi }{2}\\ e^{\frac{\cot 6x}{\cot 4x}},& \frac{\pi }{2}<x<\pi \end{array}\right.$is continuous at $x=\frac{\pi }{2}$, then $9\lambda +6 {\log }_c\mu +{\mu }^6-e^{6\lambda }$ is equal to