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  • Try this! - Limit , continuity and differentiability - JEE Main-6

\lim_{x\rightarrow \pi /4}(1+ \tan x)^{2 \sin (\pi /4+x)} equals 

  • Option 1)

    4

  • Option 2)

    2

  • Option 3)

    1

  • Option 4)

    1/2

 

Answers (1)

best_answer

As we have learned

Limit of power -

\lim_{x\rightarrow a}f(x)^{g(x)}=(P)\lim_{x\rightarrow a}g(x)


Where\:f(x)^{g(x)}\:does\:not\;take\:indeterminate\:form\:at\:x=a

- wherein

Where P is a non zero finite constant

 

 When x\rightarrow \pi /4  then (1+ \tan x)\rightarrow 2  and 2\sin (\pi /4+x)\rightarrow 2

\therefore \lim_{x\rightarrow\pi /4 }(1+ \tan x)^{2\sin (\pi /4+x)}=2^{2}=4

 

 

 

 

 


Option 1)

4

Option 2)

2

Option 3)

1

Option 4)

1/2

Posted by

Himanshu

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