Thread: Limits at x = 0?

1. Limits at x = 0?

What is the limit of $\sqrt(x-x^2)$ as $x\to 0$. I know the limit of $\sqrt(x-x^2)$ as $x\to 0+$ is 0, but since the limit doesn't exist as $x\to 0-$, is there a limit as $x\to 0$?

2. A limit $L$ exists if and only if:

$\lim_{x\to a^+} = \lim_{x\to a^-} = L$

There are more requirements, but this is what pertains to your problem.

3. So that Means No limit exists?

4. Exactly. You have to be able to arrive at the same limit from both directions. If one does not exist or is not equal to the other, then no limit exists.

5. TYVM.

6. O.K..Can one say that $f(x)=\sqrt{x-x^2}$ is continuous at x=0.

7. Originally Posted by pankaj
O.K..Can one say that $f(x)=\sqrt{x-x^2}$ is continuous at x=0.
Yes. The domain is $[0,1]$ and since $\lim_{x\to 0^+} f(x) = f(0)$ it is continous.

8. Originally Posted by ThePerfectHacker
Yes. The domain is $[0,1]$ and since $\lim_{x\to 0^+} f(x) = f(0)$ it is continous.
So the limit to my question is 0?

9. Originally Posted by kbartlett
So the limit to my question is 0?
Yes

10. Thanks