NDA MATHEMATICS QUIZ - 29

$\operatorname{Lt}_{n \rightarrow \infty}\left\{\frac{1^{2}}{n^{3}}+\frac{2^{2}}{n^{3}}+\frac{3^{2}}{n^{3}}+\ldots \ldots \ldots \ldots+\frac{1}{n}\right\}$ का मान क्या होगा ?

$\operatorname{Lt}_{x \rightarrow \infty} x\left(e^{\frac{1}{x}}-e^{-\frac{1}{x}}\right)=$

$\operatorname{Lt}_{x \rightarrow 0} \frac{(1+x)^{5}-1}{3 x+5 x^{2}}=$

$\operatorname{Lt}_{x \rightarrow 1}\left(\frac{1}{x^{2}-1}-\frac{1}{x^{4}-1}\right)=$

$\operatorname{Lt}_{x \rightarrow 0} \frac{\tan x-\sin x}{x^{3}}=$

$\operatorname{Lt}_{x \rightarrow 0} \frac{e^{\sin x}-\sin x-1}{x^{2}}=$ 

$\underset{z \rightarrow-\infty}{L t} \frac{z^{4} \sin \frac{1}{z}+z^{2}}{1+|z|^{3}}$