If $f(x) = \begin{cases} x & \text{if } x < 0 \\ 1 & \text{if } x = 0 \\ x^2 & \text{if } x > 0 \end{cases}$,then $\mathop {\lim }\limits_{x \to 0} f(x) = $

$\mathop {\lim }\limits_{x \to \frac{\pi^+}{2}} e^{[\cot x]}$ is equal to :-
(where $[.]$ is the greatest integer function)

If $I = \lim_{x \rightarrow 0} \sin \left( \frac{e^{x}-x-1-\frac{x^{2}}{2}}{x^{2}} \right)$, then the limit

If $f(x) = \begin{cases} \frac{\sin(1+[x])}{[x]}, & \text{for } [x] \neq 0 \\ 0, & \text{for } [x] = 0 \end{cases}$ where $[x]$ denotes the greatest integer function,then $\lim_{x \rightarrow 0^{-}} f(x)$ is equal to

If $[\cdot]$ denotes the greatest integer function,then $\lim _{x \rightarrow \frac{-3}{5}} \frac{1}{x}\left[\frac{-1}{x}\right]=$

$\lim _{x \rightarrow \infty}\left(1+\frac{2}{x}\right)^{3 x}=$