$\lim _{z \rightarrow 1} \frac{z^{1/3}-1}{z^{1/6}-1} = $

$\mathop {\lim }\limits_{x \to 0} \cos \frac{1}{x}$

If $\operatorname{Lim}_{x \rightarrow 0}\left(\frac{\tan x}{x}\right)^{\frac{1}{x^2}}=p$,then $96 \log _e p$ is equal to . . . . . .

Find the limit: $\mathop {\lim }\limits_{x \to 1} \frac{x^{2}+1}{x+100}$

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

$\mathop {\lim }\limits_{x \to 0} \left( {\frac{{{a^x} - {b^x}}}{x}} \right) = $