Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Help me understand! - Limit , continuity and differentiability - JEE Main-8

\lim_{x\rightarrow 0}\left ( \tan (\pi /4-x) \right )^{1/x} equals 

  • Option 1)

    e^{-2}

  • Option 2)

    e^{-1}

  • Option 3)

    1

  • Option 4)

    e

 

Answers (1)

best_answer

As we have learned

1 to the power of infinity Form -

Let\:\:\;\lim_{x\rightarrow a}f(x)^{g(x)}\:\;\:where

f(a)=1\:\:\:and \;\:\:g(a)=\infty

Then\:\:\:\:e^\lim_{x\rightarrow a}(f(x)-1)g(x)

-

 

= \lim_{x\rightarrow 0} \left ( \frac{1- \tan x}{1+ \tan x} \right )^{1/x}

                                             \left ( \because \tan (A-B) = \frac{\tan A- \tan B}{1+ \tan A \tan B} \right )

= e^{\lim_{x\rightarrow 0}\left ( \frac{1- \tan x}{1+ \tan x}-1 ) \cdot \right)1/x }

= e^{\lim_{x\rightarrow 0}\left ( \frac{-2 \tan x}{(1+ \tan x)\cdot x} ) \cdot \right)}=e^{\lim_{x\rightarrow 0}\frac{(-\tan x/x)2}{1+\tan x}}

e^{-2} 

 

 

 

 


Option 1)

e^{-2}

Option 2)

e^{-1}

Option 3)

1

Option 4)

e

Posted by

Himanshu

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

JAC Chandigarh Counselling 2025: Round 1 seat allotment result out for BTech admissions
anam-khan

JoSAA round 5 seat allotment result 2025 out on josaa.nic.in

Latest Question