Question Number 25068 by NECx last updated on 02/Dec/17
$${Evaluate}\: \\ $$$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\left(\frac{{tan}\mathrm{2}{x}}{{x}−\pi/\mathrm{2}}\right) \\ $$
Answered by jota+ last updated on 03/Dec/17
$${Use}\:{Hopital}\:{rule} \\ $$$$=\frac{\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\left({tan}\mathrm{2}{x}\right)'}{\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\left({x}−\pi/\mathrm{2}\right)^{'} }=\frac{\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\mathrm{2}/{cos}^{\mathrm{2}} \mathrm{2}{x}}{\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}1}}=\mathrm{2} \\ $$$$ \\ $$$$ \\ $$