Multivariable Calculus: When to use Squeeze Theorem to solve limits?

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


For example in:
lim (x,y) -> (0,0) [(xy^2)/(x^2+y^4)]

This limit does not exist (according to textbook), but if you use squeeze theorem since y^2<(x^2+y^4)
y^2/(x^2+y^4) <= 1 and therefore

0 <= (xy^2)/(x^2+y^4) <= x
as x--> 0
so
lim (x,y) -> (0,0) [(xy^2)/(x^2+y^4)] = 0?
 

Answers and Replies

  • #2
761
13
What happens if you look at y=sqrt(x)?
 
  • #3
364
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What happens if you look at y=sqrt(x)?

I see what you mean but what if i was looking at a different limit and I got 0 every time while using different paths. I still couldn't prove it with squeeze theorem because what if there is just this one path that i never tried.
 

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