$\lim _{x \rightarrow 0} \frac{\sin |x|}{x}$ is equal to

$\lim _{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2 x)^3}$ equals

The limit of $\sum_{n=1}^{1000} (-1)^{n} x^{n}$ as $x \rightarrow \infty$ is:

$\lim _{n}$ ${\rightarrow \infty} \frac{\left(1^2-1\right)(n-1)+\left(2^2-2\right)(n-2)+\ldots +\left((n-1)^2-(n-1)\right) \cdot 1}{\left(1^3+2^3+\ldots +n^3\right)-\left(1^2+2^2+\ldots +n^2\right)}$ is equal to:

$\lim\limits_{x \rightarrow 2} \frac{3^{x}+3^{3-x}-12}{3^{-x / 2}-3^{1-x}}$ is equal to

$\lim _{n \rightarrow \infty} \frac{\left[6^2+12^2+18^2+\ldots+(6 n)^2\right]^2}{[5+10+15+\ldots+5 n]\left[2^3+4^3+6^3+\ldots+(2 n)^3\right]} =$