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  • Try this! - Limit , continuity and differentiability - JEE Main-8

Let f(x)= \sin x , Then at x =0 f(x) is 

  • Option 1)

    continous but not diffrentiable

  • Option 2)

    continous and  diffrentiable both

  • Option 3)

    neither continous nor diffrentiable

  • Option 4)

    not continous but  diffrentiable

 

Answers (1)

best_answer

 As we have learned

Differentiability -

Let  f(x) be a real valued function defined on an open interval (a, b) and  x\epsilon (a, b).Then  the function  f(x) is said to be differentiable at   x_{\circ }   if

\lim_{h\rightarrow 0}\:\frac{f(x_{0}+h)-f(x_{0})}{(x_{0}+h)-x_{0}}


or\:\:\:\lim_{h\rightarrow 0}\:\frac{f(x)-f(x_{0})}{x-x_{0}}

-

 

 For continuity 

\lim_{x\rightarrow 0^{+}\sin x}= \lim_{x\rightarrow 0^{-}} \sin x =f(0) =0

\therefore continous at x=0 

For diffrentiabilty 

\because f(x)  is continous at x= 0 , so we will find \lim_{x\rightarrow 0}\frac{f(x)-f(0)}{x-0}=\lim_{x\rightarrow 0}\frac{\sin x-0}{x-0}=1= finite

\therefore above limit exists so diffrentiable at x= 0   

 

 

 

 


Option 1)

continous but not diffrentiable

Option 2)

continous and  diffrentiable both

Option 3)

neither continous nor diffrentiable

Option 4)

not continous but  diffrentiable

Posted by

Himanshu

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