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Evaluating a limit of a function of two variables

  1. Jul 9, 2015 #1
    I want to evaluate [itex]\displaystyle\lim_{(x,y)\to(-1,0)}\frac{y^4(x+1)}{|x+1|^3+2|y|^3}[/itex]

    With some help, I was able to prove that the limit is 0, using Hölder's inequality. Like this:


    Raising to the [itex]5/3[/itex] power and cancelling we get:


    But I wonder if there are any other ways to prove it. Does anyone have other ideas?

    Thanks for any input.
  2. jcsd
  3. Jul 10, 2015 #2
    We used to use the word DANG to remind students of the four ways to approach limits:

    Direct substitution
    Algebraic manipulation
    Numerical approximation
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