If $f(x) = \sqrt{\frac{x - \sin x}{x + \cos^{2} x}}$,then $\lim_{x \rightarrow \infty} f(x)$ is

Let $a_{1}, a_{2}, \dots, a_{n}$ be fixed real numbers and define a function $f(x) = (x - a_{1})(x - a_{2}) \dots (x - a_{n})$. What is $\lim_{x \to a_{1}} f(x)$? For some $a \neq a_{1}, a_{2}, \dots, a_{n}$,compute $\lim_{x \to a} f(x)$.

The value of $\lim\limits_{n \rightarrow \infty} 6 \tan \left\{\sum\limits_{r=1}^{n} \tan ^{-1}\left(\frac{1}{r^{2}+3 r+3}\right)\right\}$ is equal to

$\lim _{n \rightarrow \infty} \frac{2^2+4^2+6^2+\ldots+(2 n)^2}{n^3} = $

$\mathop {\lim }\limits_{n \to \infty } \left[ {\frac{{\sum_{k=1}^{n} {k^2}}}{{{n^3}}}} \right] = $

$\mathop {\lim }\limits_{x \to 0} \frac{{\sin (2 + x) - \sin (2 - x)}}{x} = $