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

1. ## 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.

2. ## Re: find all points that lim f(x) doesn't exist

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

3. ## Re: find all points that lim f(x) doesn't exist

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

4. ## Re: find all points that lim f(x) doesn't exist

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 $\displaystyle \pm \infty$?