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  • Stuck here, help me understand: - Limit , continuity and differentiability - JEE Main-10

Let f(x)=\left \{ 1/|x| ; x\neq 0 \right.

                       \left \{ 0 ; x=0 \right.   then at x=0

  • Option 1)

    f(x) is continous 

  • Option 2)

    f(x) has removable discontinuty

  • Option 3)

    f(x) is continous from right of x=0

  • Option 4)

    f(x) has infinite non removable discontinuty 

 

Answers (1)

best_answer

As we have learned

Infinite irremovable discontinuity -

A function f is said to possess discontinuity at  x = a the left hand limit and right hand limit both do not exist and infinite.

- wherein

 

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

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

LHL and RHL both are infinite

 

 

 

 

 


Option 1)

f(x) is continous 

Option 2)

f(x) has removable discontinuty

Option 3)

f(x) is continous from right of x=0

Option 4)

f(x) has infinite non removable discontinuty 

Posted by

Himanshu

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