You don't need to use scientific notation in evaluating this limit.

All you're looking for is the signs on top & on the bottom.

Now, I would guess you are not fully aware of what I wrote because in the limit you've provided you've mixed it up.

\(\displaystyle \lim_{x \to -1^-} [ \frac{x^3}{x^2 - 1}]\)

There is a subtlety here, in \(\displaystyle \lim_{x \to -1^-}\) do you see the minus on top of the (-1)?

This means that you use the number line & go from -∞ towards -1, i.e. if you substitute in -2 it will work here because all you're interested in is the sign.

The minus there means that you approach whatever the limit is **from** that side.

\(\displaystyle \lim_{x \to -1^-}\) approach (-1) from the negative side & increase towards the positive side.

\(\displaystyle \lim_{x \to -1^+}\) approach (-1) from the **positive** side & go down towards the negative side.

Also, about the asymptote, you see that Mr. Fantastic gave you

\(\displaystyle \frac{x^3}{x^2 - 1} = x + \frac{x}{x^2 - 1}\)

well he just used **long division** to reduce the original equation into an equivalent equation but it cannot be used at (-1) or 1 because the original function is **undefined** there.

This should be instantly recognisable because the degree in the numerator is **one higher** than that of the denominator.

When you see this type of function you use long division to reduce it to an equivalent equation & the first term that is your asymptote, (in this case x!).

The function is well defined at 0, it is equal to zero!