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  • How to solve this problem- - Limit , continuity and differentiability - JEE Main-8

Let f(x)\left \{ \frac{|x|}{x} ; x\neq 0 : k ; x=0 \right.    then          

                             

  • Option 1)

    If k= 1 , f(x ) becomes continous at x= 0

  • Option 2)

    If k= -1 , f(x ) becomes continous at x= 0

  • Option 3)

    for no value of k , f(x) can be made continous at x=0

  • Option 4)

    f(x) is continous at x= 0 , for all value of k

 

Answers (1)

best_answer

As we have learned

Irremovable discontinuity -

A function f is said to possess irremovable discontinuity if at  x = a the left hand limit is not equal to the right hand limit so limit does not exist  L\neq R

\lim_{x\rightarrow a^{-}}\:f(x)\neq \lim_{x\rightarrow a^{+}}\:f(x)

-

 

 LHL=\lim_{x\rightarrow 0^{-}}\frac{|x|}{x}=-1

RHL=\lim_{x\rightarrow 0^{+}}\frac{|x|}{x}=1

f(0)=k

Limit doesn't exist  , f(x) has irremovable discontinuty , so ffor no 'k' it will be continous  

 


Option 1)

If k= 1 , f(x ) becomes continous at x= 0

Option 2)

If k= -1 , f(x ) becomes continous at x= 0

Option 3)

for no value of k , f(x) can be made continous at x=0

Option 4)

f(x) is continous at x= 0 , for all value of k

Posted by

Himanshu

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