# find all points that lim f(x) doesn't exist

• Oct 1st 2011, 09:33 PM
apple2009
find all points that lim f(x) doesn't exist
I found one of the points a=3, but I can't find the others.Attachment 22465
• Oct 1st 2011, 10:08 PM
Prove It
Re: find all points that lim f(x) doesn't exist
Quote:

Originally Posted by apple2009
I found one of the points a=3, but I can't find the others.Attachment 22465

A function is only continuous at a point if the limit exists at that point, and if this limit is equal to the function value at this point.
Polynomials are continuous over their given domains. So for this hybrid function of polynomials, it may only be discontinuous where the function changes from one polynomial to another. At what points does this happen? Check the left and right hand limits of the function at those points. The limit only exists at that point if the left and right-hand limits are the same...
• Oct 1st 2011, 10:38 PM
CaptainBlack
Re: find all points that lim f(x) doesn't exist
Quote:

Originally Posted by Prove It
A function is only continuous at a point if the limit exists at that point, and if this limit is equal to the function value at this point.
Polynomials are continuous over their given domains. So for this hybrid function of polynomials, it may only be discontinuous where the function changes from one polynomial to another. At what points does this happen? Check the left and right hand limits of the function at those points. The limit only exists at that point if the left and right-hand limits are the same...

The limits at +/-infinity may also not exist

CB
• Oct 1st 2011, 10:45 PM
Prove It
Re: find all points that lim f(x) doesn't exist
Quote:

Originally Posted by CaptainBlack
The limits at +/-infinity may also not exist

CB

And how are you supposed to evaluate left and right hand limits at $\displaystyle \displaystyle \pm \infty$?