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Limits of 2 variables

  1. Mar 31, 2008 #1
    What is:
    lim(x,y)->(0,0) of (x^2)(y) / ((x^4) + (y^2)) ?

    When I take x_n = 0, y_n = 1/n, lim=0
    and x_n = 1/n, y_n = 0, lim=0
    and x_n = y_n = 1/n, lim=0
    All three limits are zero, yet other people I've asked say the limit doesn't
    exist. Am I right, or am I doing something wrong here? Thanks.
  2. jcsd
  3. Mar 31, 2008 #2
    [tex]\lim_{(x,y) \rightarrow (0,0)}\frac{x^2y}{x^4+y^2}[/tex]

    [tex]\lim_{(x,y) \rightarrow (0,0)}\frac{0\cdot y}{0+y^2}=0[/tex]

    [tex]\lim_{(x,y) \rightarrow (0,0)}\frac{x^2\cdot 0}{x^4+0}=0[/tex]

    [tex]\lim_{(x,x^2) \rightarrow (0,0)}\frac{x^4}{2x^4}=\frac 1 2[/tex]

    Aim to make your powers the same, use [tex]y=x^2[/tex] or [tex]x=y^2[/tex].

    General tests:

    Last edited: Mar 31, 2008
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