The value of $\lim _{x \rightarrow 0} \left( \frac{x}{\sqrt[8]{1-\sin x}-\sqrt[8]{1+\sin x}} \right)$ is equal to:

Evaluate the limit: $\lim _{x \rightarrow \infty}\left\{x-\sqrt[n]{\left(x-a_1\right)\left(x-a_2\right) \ldots\left(x-a_n\right)}\right\}$, where $a_1, a_2, \ldots, a_n$ are positive rational numbers.

For a certain value of $c$, $\mathop {Lim}\limits_{x \to - \infty } [(x^5 + 7x^4 + 2)^c - x]$ is finite and non-zero. The value of $c$ and the value of the limit are:

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

$\lim _{x \rightarrow \infty}\left(\sqrt[3]{x^3+4 x^2}-\sqrt{x^2-3 x}\right)=$

The value of $f(0)$ so that the function $f(x) = \frac{(256 - 8x)^{\frac{1}{4}} - 4}{16 - 4(64 + 3x)^{\frac{1}{3}}}$, $x \neq 0$ is continuous at $x = 0$, is