# Limits

• Dec 3rd 2008, 06:44 PM
EricaMae
Limits
Hi!

This isn't too bad, but I just want to make sure that I have this right.

I'm trying to find the

limit (as h->0) of (yh^3-hy^3)/(h^3+hy^2)

I'm getting -hy. But next I need to calculate the second partial derivative (which was what I was doing in the first place using the limit definition) with respect to y. But obviously I'm getting 0, which I don't think is right.

Thanks!
• Dec 3rd 2008, 07:00 PM
terr13
If h is going to 0, and you are getting the limit to be -hy, doesn't that mean that it is 0?
• Dec 3rd 2008, 07:39 PM
Mathstud28
Quote:

Originally Posted by EricaMae
Hi!

This isn't too bad, but I just want to make sure that I have this right.

I'm trying to find the

limit (as h->0) of (yh^3-hy^3)/(h^3+hy^2)

I'm getting -hy. But next I need to calculate the second partial derivative (which was what I was doing in the first place using the limit definition) with respect to y. But obviously I'm getting 0, which I don't think is right.

Thanks!

\displaystyle \begin{aligned}\lim_{h\to{0}}\frac{yh^3-hy^3}{h^3+hy^2}&=\lim_{h\to{0}}\frac{yh^2-y^3}{h^2+y^2}\\ &=-y\end{aligned}