$\mathop {\lim }\limits_{x \to - 2} \frac{{{{\sin }^{ - 1}}(x + 2)}}{{{x^2} + 2x}}$ is equal to

If $f(x)$ is a differentiable function and $f''(0) = a$,then $\mathop {\lim }\limits_{x \to 0} \frac{2f(x) - 3f(2x) + f(4x)}{x^2}$ is (in $a$)

The value of $\mathop {\lim }\limits_{x \to \pi /4} \frac{{{{\cot }^3}x - \tan x}}{{\cos \left( {x + \pi /4} \right)}}$ is

If $l_1 = \lim_{x \rightarrow 2^{+}} (x + [x])$,$l_2 = \lim_{x \rightarrow 2^{-}} (2x - [x])$ and $l_3 = \lim_{x \rightarrow \pi/2} \frac{\cos x}{x - \pi/2}$,then:

Evaluate the limit: $\lim _{x \rightarrow 0^{+}}\left(e^{x}+x\right)^{1 / x}$

$\mathop {\lim }\limits_{x \to 0} \frac{{\sin x - x}}{{{x^3}}} = $