does anyone know how to sole this limit WITHOUT using L'Hôpital's rule? lim as x -- 1 from the right side, the function is -4/cube root of (1-x^2)

Question

does anyone know how to sole this limit WITHOUT using L'Hôpital's rule?  lim as x --> 1 from the right side, the function is  -4/cube root of (1-x^2)

anonymous · Answer

infinite

rogue · Answer

$$\lim_{x \rightarrow 1} \frac {-4}{\sqrt[3]{1 - x^2}}$$

rogue · Answer

Does the limit exist first of all?

anonymous · Answer

Hey Rogue, it is a right sided limit, but I think Ackhat may have nailed it.  It makes sense that it would go to positive infinity.  I think.

anonymous · Answer

Thanks for your time Rogue and Ackhat.  I greatly appreciate it.

rogue · Answer

Yeah, it is infinity if approached from the right. However, the over limit does not exist since the right & left limits are not equal. There really isn't any other way of doing this algebraically with out L'Hopital's, although you might be able to see it intuitively.