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Let a function be given as f(x)=3-2x if x is less than or equal to 1..and f(x)=3x-5 if x>1..Find the limit as x tends to 1..On evaluation it is found that the Left Hand Limit (LHL) comes out to be 1 and the Right Hand Limit (RHL) is -2..My question is since LHL is not equal to RHL,can I say that the limit x tends to 1 f(x) does not exist? Please elucidate.

Let a function be given as f(x)=3-2x if x is less than or equal to 1..and f(x)=3x-5 if x>1..Find the limit as x tends to 1..On evaluation it is found that the Left Hand Limit (LHL) comes out to be 1 and the Right Hand Limit (RHL) is -2..My question is since LHL is not equal to RHL,can I say that the limit x tends to 1 f(x) does not exist? Please elucidate.

Grade:Upto college level

1 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
11 years ago

Dear Aniket

For a limit to exist at a point left hand limit must be equal to right hand limit. hence limit does not exist at x=1

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IITD

 

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