Evaluate the given limit: $\mathop {\lim }\limits_{x \to 2} \frac{3x^{2}-x-10}{x^{2}-4}$

$\mathop {\lim }\limits_{x \to 0} \frac{{{{(1 + x)}^5} - 1}}{{{{(1 + x)}^3} - 1}} = $

The value of $\mathop {\lim }\limits_{x \to \infty } \frac{(x + 1)(3x + 4)}{x^2(x - 8)}$ is equal to

The value of $\mathop {\lim }\limits_{x \to 0} \left( \left[ \frac{100x}{\sin x} \right] + \left[ \frac{99 \sin x}{x} \right] \right)$,where $[.]$ denotes the greatest integer function,is

For the function $f(x) = (1 + \frac{1}{x})^x$,which of the following limits tends to unity?

Find the limit: $\mathop {\lim }\limits_{x \to 3} [x(x+1)]$