1. Limits!!!!

47. f(x)= {x^3 if x cant equal 1
0 if x =1

find lim x->1^- f(x) and lim x->1^+ f(x)

Does lim x->1^ f(x) exist? If so, what is it? If not, why not?

2. Re: Limits!!!!

Is the function continuous at x=1?

3. Re: Limits!!!!

Originally Posted by Kathrynm77
47. f(x)= {x^3 if x cant equal 1
0 if x =1
find lim x->1^- f(x) and lim x->1^+ f(x)
Does lim x->1^ f(x) exist? If so, what is it? If not, why not?
$\lim _{x \to 1^ - } x^3 = \lim _{x \to 1^ + } x^3 = 1$ SO?

4. Re: Limits!!!!

Originally Posted by Kathrynm77
47. f(x)= {x^3 if x cant equal 1
0 if x =1

find lim x->1^- f(x) and lim x->1^+ f(x)
Have you made any attempt at this at all? It's pretty close to trivial!

Does lim x->1^ f(x) exist? If so, what is it? If not, why not?
What do you mean by "lim x->1^ f(x)"? Just the limit itself? You don't need the "^" in that case.
you should have learned that " $\lim_{x\to a} f(x)$ exist if and only if both $\lim_{x\to a^-} f(x)$ and $\lim_{x\to a^+} f(x)$ exist and are the same".

5. Re: Limits!!!!

I have some video tutorials on limits on my youtube channel. the first video is at: https://www.youtube.com/watch?v=Xw8lWFI7viY. hope that helps.