$\lim _{y \rightarrow 1}\left(\frac{1}{y^2-1}-\frac{2}{y^4-1}\right)=$

If $x_1 = 3$ and $x_{n+1} = \sqrt{2 + x_n}$ for $n \ge 1$,then $\lim_{n \to \infty} x_n$ is equal to

$\mathop {\lim }\limits_{n \to \infty } {({4^n} + {5^n})^{1/n}}$ is equal to

$\lim _{z \rightarrow 1} \frac{z^{1/3}-1}{z^{1/6}-1} = $

The value of $\operatorname{Lt}_{x \rightarrow 0} \frac{\sin^2 x + \cos x - 1}{x^2}$ is

Let $[x]$ denote the greatest integer less than or equal to $x$. Then $\lim _{x \rightarrow 2^{+}}\left(\frac{[x]^3}{3}-\left[\frac{x}{3}\right]^3\right)=$