Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Need explanation for: - Limit , continuity and differentiability - JEE Main

   If   \lim_{x\rightarrow \infty }\left ( 1 + \frac{a}{x} - \frac{4}{x^{2}} \right )^{2x} = e^{3}  , then  'a' is equal to :

  • Option 1)

     2

  • Option 2)

    \frac{3}{2}

  • Option 3)

    \frac{2}{3}

  • Option 4)

    \frac{1}{2}

 

Answers (2)

best_answer

As we learnt in 

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 \infty }\left ( 1+\frac{a}{x}-\frac{4}{x^{2}} \right )^{2x}=e^{3}

It is 1^{\infty } form.

\therefore \lim_{x\rightarrow \infty }\left ( 1+\frac{a}{x}-\frac{4}{x^{2}}-1 \right )\times 2x

\therefore \lim_{x\rightarrow \infty }\left ( \frac{a}{x}-\frac{4}{x^{2}} \right )\times 2x

\therefore \lim_{x\rightarrow \infty }\left ( a-\frac{4}{x} \right )\cdot 2

\therefore 2a

\therefore e^{2a}=e^{3}

\therefore a=\frac{3}{2} 

 


Option 1)

 2

This option is incorrect.

Option 2)

\frac{3}{2}

This option is correct.

Option 3)

\frac{2}{3}

This option is incorrect.

Option 4)

\frac{1}{2}

This option is incorrect.

Posted by

divya.saini

View full answer

JEE Main high-scoring chapters and topics

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

Option 2

Posted by

Pushpak Sivasai. Bayana Siva Sai

View full answer

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year
anam-khan

JEE Mains: Farmer's son from remote Maharashtra village aces exam

Latest Question