limite X rightarrow 0 {tan(pi/4+x)} 1/x


$\lim _{x \rightarrow 0}\left(\tan \left(\frac{\pi}{4}+x\right)\right)^{1 / x}$ is equal to :

  1. 2

  2. $\mathrm{e}$

  3. 1

  4. $\mathrm{e}^{2}$

Correct Option: , 4


$\lim _{x \rightarrow 0}\left\{\tan \left(\frac{\pi}{4}+x\right)\right\}^{1 / x}$

$=\lim _{x \rightarrow 0} \frac{1}{x}\left\{\tan \left(\frac{x}{4}+x\right)-1\right\}$

$=e^{\lim _{x \rightarrow 9}\left(\frac{1+\tan x-1+\tan x}{x(1-\tan x)}\right)}$

$=\lim _{x \rightarrow x(1-\tan x)}$


Leave a comment


Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now