$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{{a^{\cot x}} - {a^{\cos x}}} \over {\cot x - \cos x}},a > 0$$

Rolle's theorem is not applicable to the function $$f(x) = |x|$$ for $$ - 2 \le x \le 2$$ because

The value of the limit $$\mathop {\lim }\limits_{x \to 2} {{{e^{3x - 6}} - 1} \over {\sin (2 - x)}}$$ is

The $$\mathop {\lim }\limits_{x \to 2} {5 \over {\sqrt 2 - \sqrt x }}$$ is