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  • Answer please! - Limit , continuity and differentiability - JEE Main-6

\lim_{x\rightarrow 0}[\frac{2 \sin x}{x}]  equals ([.]=GIF) 

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    3

  • Option 4)

    4

 

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{\sin x}{x}\rightarrow 1 but is less than one so \left [ \frac{2\sin x}{x} \right ]=1

 

 

 

 

 


Option 1)

1

Option 2)

2

Option 3)

3

Option 4)

4

Posted by

Himanshu

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