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  • Need explanation for: - Limit , continuity and differentiability - JEE Main-7

\lim_{x\rightarrow 0}\left [ \frac{3 \tan x}{x} \right ]  equals ([.]= G.I.F)

  • Option 1)

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  • Option 2)

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  • Option 3)

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  • Option 4)

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Answers (1)

best_answer

As we have learned

Condition of Trigonometric Limits -

\lim_{x\rightarrow 0}\:\:\:\frac{sinx}{x}=1\:(it\:is\:less\:than\:1)


\lim_{x\rightarrow 0}\:\:\:\frac{tanx}{x}=1\:(it\:is\:more\:than\:1)

- wherein

because\:\:\:\:\:\frac{sinx}{x}<1

                    
                      \frac{tanx}{x}>1

 

 when x\rightarrow 0, \frac{\tan x}{x}\rightarrow 1,  but is  more than 1 

so \frac{3\tan x}{x}\rightarrow 3, but will be more than 3

so limit = 3

 

 

 

 


Option 1)

1

Option 2)

2

Option 3)

3

Option 4)

4

Posted by

Himanshu

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