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How to solve this problem- - Limit , continuity and differentiability - JEE Main-7

\lim_{x\rightarrow \pi /6} \tan^{4}x equals 

  • Option 1)

    1/3

  • Option 2)

    1/9

  • Option 3)

    1/27

  • Option 4)

    1/81

 
Answers (1)
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As we have learned

Limit of power -

Limit of power equals the power of limit provided the power function does not takes any indeterminate form.

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

Provided    \lim_{x\rightarrow a}f(x)  exist finitely end is non zero

- wherein

where k is non zero constant.

 

 As x approaches \pi/6 then  \tan x approaches \tan (\pi /6) i.e 1/ \sqrt 3 

\therefore \lim_{x\rightarrow \pi /6}(\tan x)^{4} = \left ( \frac{1}{\sqrt3} \right )^{4}=1/9

 

 

 

 

 


Option 1)

1/3

Option 2)

1/9

Option 3)

1/27

Option 4)

1/81

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