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Limit and Continuity

  • Thread starter ahhppull
  • Start date
  • #1
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Homework Statement


lim of (y^2)(sin^2x) /(x^4+y^4) as (x,y) approaches (0,0)


Homework Equations





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
 

Answers and Replies

  • #2
115
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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