Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Find the Value of   <img alt="\mathrm{\lim _{x \rightarrow 0} \frac{x-\tan (x)}{x-\sin (x)} }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Clim%20_%7Bx%20%5Crightar

Find the Value of   \mathrm{\lim _{x \rightarrow 0} \frac{x-\tan (x)}{x-\sin (x)} }

Option: 1

0


Option: 2

1


Option: 3

-2


Option: 4

2


Answers (1)

best_answer

\mathrm{\lim _{x \rightarrow 0} \frac{x-\tan (x)}{x-\sin (x)}}

This is a \frac{0}{0} indeterminate form, hence L'hospitals rule is applicable;

\mathrm{=\lim _{x \rightarrow 0} \frac{1-\sec ^2(x)}{1-\cos (x)}}

applying L'Hospitals rule once again gives;

\begin{aligned} &\mathrm{ =\lim _{x \rightarrow 0} \frac{-2 \sec ^2(x) \tan (x)}{\sin (x)} }\\ &\mathrm{ =\lim _{x \rightarrow 0} \frac{-2 \sec ^3(x) \cdot \sin (x)}{\sin (x)} }\\ &\mathrm{ =\lim _{x \rightarrow 0}-2 \sec ^3(x) }\\ &\mathrm{ =-2}\\ \end{aligned}

Posted by

Ajit Kumar Dubey

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Mains 2026 LIVE: NTA session 2 city slip soon; exam details, marking scheme, prep tips
anam-khan

JEE Main 2026: NTA reopens Session 2 registration; apply by March 13 at jeemain.nta.nic.in
anam-khan

JEE Mains 2026 LIVE: NTA session 2 city slip soon; admit card, exam dates, here's how to prepare

Latest Question