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  • Give answer! - Limit , continuity and differentiability - JEE Main-5

\lim_{x\rightarrow 0}(1+ \sin x)^{\cot x}  equals

  • Option 1)

    1

  • Option 2)

    e

  • Option 3)

    e^{2}

  • Option 4)

    e^{3}

 

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)

-

 

 liimit = e^{\lim_{x\rightarrow 0}} (1+\sin x-1)\cdot \frac{\cos x}{\sin x}=e^{\lim_{x\rightarrow 0}\cos x}= e^{1}= e

 

 

 

 

 


Option 1)

1

Option 2)

e

Option 3)

e^{2}

Option 4)

e^{3}

Posted by

Himanshu

View full answer

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