Find the limit: $\mathop {\lim }\limits_{x \to 1} (x^3 - x^2 + 1)$

The value of $\mathop {\lim }\limits_{x \to 0} \frac{1}{x}\left[ {{{\tan }^{ - 1}}\left( {\frac{{x + 1}}{{2x + 1}}} \right) - \frac{\pi }{4}} \right]$ is

If $\mathop {\lim }\limits_{x \to a} \frac{{{x^9} + {a^9}}}{{x + a}} = 9$,then $a = $

Let $[x]$ denote the greatest integer less than or equal to $x$ and $f(x) = 2x - [2x]$. If $\lim_{x \rightarrow 2^{-}} f(x) = l_1$ and $\lim_{x \rightarrow 2^{+}} f(x) = l_2$,then $l_1 + l_2 =$

Let for all $x > 0$, $f(x) = \lim_{n \rightarrow \infty} n(x^{1/n} - 1)$, then

Evaluate the given limit: $\mathop {\lim }\limits_{x \to -2} \frac{\frac{1}{x} + \frac{1}{2}}{x + 2}$