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Math Help - Limits

  1. #1
    Junior Member
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    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!
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  2. #2
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    If h is going to 0, and you are getting the limit to be -hy, doesn't that mean that it is 0?
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by EricaMae View Post
    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!
    \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}\\<br />
&=-y\end{aligned}
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