If the real valued function $f(x)=\int \frac{\left(4^{x}-1\right)^{4} \cot (x \log 4)}{\sin (x \log 4) \log \left(1+x^{2} \log 4\right)}, \quad$ if $x \neq 0$ is continuous at $x=0$, then $e^{k}=$

If $0 \leq x \leq \frac{\pi}{2}$, then $\lim _{x \rightarrow a} \frac{|2 \cos x-1|}{2 \cos x-1}$

The real valued function $f(x)=\frac{|x-a|}{x-a}$ is

If $f(x)=3 x^{15}-5 x^{10}+7 x^{5}+50 \cos (x-1)$, then $\lim\limits_{h \rightarrow 0} \frac{f(1-h)-f(1)}{h^{3}+3 h}$