91Ó°ÊÓ

\text { Draw the graph of function } f(x)=\frac{|x|}{x} . \text { Is } f(0) \text { defined? Does } \lim _{x \rightarrow 0} f(x) \text { exist? \\{Ans. No, No\\} }

$$ \left.\lim _{x \rightarrow 0} \frac{\tan 2 x}{\sin 5 x} \text { \\{Ans. } \frac{2}{5}\right\\} $$

$$ \left.\lim _{x \rightarrow \infty} \sqrt{x^{2}+x+1}-\sqrt{x^{2}+1} . \text { \\{Ans. } \frac{1}{2}\right\\} $$

$$ \lim _{x \rightarrow \infty}\left(\frac{x^{2}+2 x-1}{2 x^{2}-3 x-2}\right)^{\frac{2-1}{-1}} \quad\left\\{\text { Ans. } \frac{1}{4}\right\\} $$

$$ \lim _{x \rightarrow 0}\left(1+\tan ^{2} \sqrt{x}\right)^{\frac{1}{2 x}}\\{\text { Ans. } \sqrt{e}\\} $$

$$ \lim _{x \rightarrow 0} \frac{\sqrt{1-\cos 2 x}}{x}\\{\text { Ans. } \sqrt{2},-\sqrt{2}\\} $$

$$ \lim _{x \rightarrow 0} \frac{3 x+|x|}{7 x-5|x|} \cdot\left\\{\text { Ans. } 2, \frac{1}{6}\right\\} $$

$$ \lim _{x \rightarrow 1} \frac{1-4 \sin ^{2}\left(\frac{\pi x}{6}\right)}{1-x^{2}}\left\\{\text { Ans. } \frac{\pi \sqrt{3}}{6}\right\\} $$