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  • Solve! - Limit , continuity and differentiability - JEE Main-8

 

f(x)= \left \{x+2 ; x\leq 1

                 \left \{ : 3-x ;x> 1\right. \right.

then at x=1   

  • Option 1)

    f(x) is continous 

  • Option 2)

    f(x) has removable discontinuty

  • Option 3)

    f(x) has finite  non-removable discontinuty

  • Option 4)

    f(x) is continous to right of x= 1

 

Answers (1)

best_answer

As we have learned

Finite irremovable discontinuity -

A function f is said to possess discontinuity at  x = a  if at   x = a the left hand limit both exist finitely but are unequal.

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

- wherein

 

 

LHL=\lim_{x\rightarrow 1^{-}}x+2=3; RHL =\lim_{x\rightarrow 1^{+}}3-x=2;f(1)=3

LHL\neq RHL so limit doesn't exist but they are finite non reremovable disconinuty at x= 1

 

 

 

 


Option 1)

f(x) is continous 

Option 2)

f(x) has removable discontinuty

Option 3)

f(x) has finite  non-removable discontinuty

Option 4)

f(x) is continous to right of x= 1

Posted by

Himanshu

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