$\mathop {\lim }\limits_{x \to 0} \frac{{{{(27 + x)}^{\frac{1}{3}}}} - 3}{{9 - {{(27 + x)}^{\frac{2}{3}}}}}$ equals.

If $f(9)=9$ and $f^{\prime}(9)=4$,then $\lim _{x \rightarrow 9} \frac{\sqrt{f(x)}-3}{\sqrt{x}-3}=$

$\mathop {Limit}\limits_{x \to 0} {(\cos 2x)^{3/x^2}}$ has the value equal to . . . . . . .

Evaluate the limit: $\lim _{x \rightarrow 0} \frac{e^x-e^{\sin x}}{2(x-\sin x)}$

Let $f: R \rightarrow R$ be a continuous function. Then $\lim _{x \rightarrow \frac{\pi}{4}} \frac{\frac{\pi}{4} \int_{2}^{\sec ^{2} x} f(t) dt}{x^{2}-\frac{\pi^{2}}{16}}$ is equal to :

The value of $\mathop {\lim }\limits_{x \to 0} \frac{{x\cos x - \log (1 + x)}}{{{x^2}}}$ is