1. ## One sided limits.

Find: $\displaystyle \lim_{x\to 0-}\sqrt{x^3-x}$.

Our teacher said that the limit exists for this function namely, 0, but our book tells that the limit doesn't exist.
He argued that the limit exists because the domain of the function is $\displaystyle [-1,0]\cup[1,\infty)$
which includes negative nos. from -1 to zero (less than -1 will make the function imaginary).

Which is correct?

2. ## Re: One sided limits.

Teacher is correct because if you take 0-h as h->0, the function is well defined in the neighborhood and also defined at x=0. So LHL does exist.

3. ## Re: One sided limits.

Originally Posted by Kaloda
Find: $\displaystyle \lim_{x\to 0-}\sqrt{x^3-x}$.

Our teacher said that the limit exists for this function namely, 0, but our book tells that the limit doesn't exist.

4. ## Re: One sided limits.

@emakarov:

Yea, because it's a question in a practice test so the book gives only the answer and not the solution.

5. ## Re: One sided limits.

I agree with pratique and your teacher that the limit exists.