The value of $\lim _{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2 x)^3}$ is

Consider the function $g(x)$ defined as

$$ g(x)=\left\{\begin{array}{cc} \frac{x^2-4}{x^2-2|x-2|-4}, & x \neq 2 \\ \frac{3}{4}, & x=2 \end{array}\right. $$

Which of the following statements is true about the continuity of $g(x)$ ?

If $\mathop {\lim }\limits_{x \to \infty }\left\{\frac{x^2-1}{x+1}-a x-b\right\}=2$. The value of $a$ is

Let $ f $ be the function defined by

$ f(x)=\left\{\begin{array}{cc} \frac{x^{2}-1}{x^{2}-2|x-1|-1}, & x \neq 1 \\ \frac{1}{2}, & x=1 \end{array}\right. $