NDA MATHEMATICS QUIZ - 30

$\operatorname{Lim}_{x \rightarrow \frac{\pi}{2}} \frac{a^{\cot x}-a^{\cos x}}{\cot x-\cos x}=\ldots . .$

$=\operatorname{Lim}_{x \rightarrow 0} \frac{\tan -x}{x^{2} \tan x}=\ldots \ldots$

$L_{x \rightarrow 0} \frac{2 \tan x-\sin 2 x}{x^{3}}=\ldots \ldots .$

$\operatorname{Lt}_{x \rightarrow 0}\left(\frac{1+7x^{2}}{1+3 x^{2}}\right)^{\frac{1}{x^{2}}}=\ldots \ldots$

$\operatorname{Lt}_{x \rightarrow \infty}\left(\frac{x+4}{x+1}\right)^{x+3}=\ldots \ldots$

$\operatorname{Lt}_{x \rightarrow \infty}\left\{\frac{1^{\frac{1}{x}}+2^{\frac{1}{x}}+3^{\frac{1}{x}}+. .+. .+n^{\frac{1}{x}}}{n}\right\}^{n x}$ equals:

$\operatorname{Lim}_{x \rightarrow 0}\left\{\tan \left(\frac{\pi}{4}+x\right)\right\}=\ldots \ldots$

$\operatorname{Lt}_{x \rightarrow 0} \frac{x \cos x-\log (1+x)}{x^{2}}$ equals:

$\operatorname{Lt}_{x \rightarrow 0} \frac{x. 2^{x}-x}{1-\cos x}=\ldots$

$\operatorname{Lim}_{x \rightarrow 0} \frac{2 e^{x}-1-x^{2}}{x^{3}}=\ldots \ldots$