$\lim\limits_{x \rightarrow \frac{3}{2}} \frac{\left(4 x^{2}-6 x\right)\left(4 x^{2}+6 x+9\right)}{\sqrt[3]{2 x}-\sqrt[3]{3}}=$

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