$\mathop {\lim }\limits_{x \to 1} \frac{{\log x}}{{x - 1}} = $

If $f(0) = 2,$ then $\mathop {\lim }\limits_{x \to 0} \frac{{\int\limits_0^x {\left( {tf(x) + xf(t)} \right)dt} }}{{{x^2}}}$ is equal to -

The value of the limit $\mathop {\lim }\limits_{x \to 0} \frac{{{e^x} - {e^{ - x}} - 2x}}{{x - \sin x}}$ is

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

$\lim _{x \rightarrow \pi / 2}(\sec x-\tan x)$ is equal to

If $\lim _{t}$ ${\rightarrow 0}\left(\int_0^1(3 x+5)^t d x\right)^{\frac{1}{t}}=\frac{\alpha}{5 e}\left(\frac{8}{5}\right)^{\frac{2}{3}}$,then $\alpha$ is equal to . . . . . .