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  • Can someone help me with this, - Limit , continuity and differentiability - JEE Main-8

Let f(x) = \left \{ [x] ; x\neq 1: 1 ; x=1 \right.       then at x=1 

  • Option 1)

    f(x) is continous 

  • Option 2)

    f(x) is continous from left 

  • Option 3)

    f(x) has non - removable discontinuity 

  • Option 4)

    f(x) has removable discontinuty

 

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 1^{-}}[x]=0 ;RHL =\lim_{x\rightarrow 1^{+}}[x]=1 ;f(1)=[1]=1

\therefore (A),(B),(D)  are false

 

 

 

 


Option 1)

f(x) is continous 

Option 2)

f(x) is continous from left 

Option 3)

f(x) has non - removable discontinuity 

Option 4)

f(x) has removable discontinuty

Posted by

Himanshu

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