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Limit and Continuity

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data
    lim of (y^2)(sin^2x) /(x^4+y^4) as (x,y) approaches (0,0)


    2. Relevant equations



    3. The attempt at a solution

    I got the limit as (x,y) approaches (0,y) and as (x,y) approaches (x,0), and it equals 0. But now I'm unsure of what to to next. I think it was the limit as (x,y) approaches (x,x) when x=y, but i get sin^2x / 2x^2
     
  2. jcsd
  3. Sep 27, 2012 #2
    [tex]\lim_{x\to 0}\frac{\sin^2x}{2x^2}=\frac{1}{2}\lim_{x\to 0}\left(\frac{\sin x}{x}\right)^2=\frac{1}{2}[/tex]
     
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