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Solving limit with three variables

  1. Apr 9, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]\lim_{(x,y,z) \to (0,0,0)} \frac {x^3 + y^3 + z^3} {x^2 + y^2 + z^2}[/tex]

    2. Relevant equations
    3. The attempt at a solution

    I believe the limit is going to 0, but I have yet to find a way to prove this is the case.
     
  2. jcsd
  3. Apr 9, 2009 #2

    Dick

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    Let x^2+y^2+z^2=r^2. Then as (x,y,z)->(0,0,0), r->0. But e.g. |x|<r. Do you see what I'm saying?
     
  4. Apr 9, 2009 #3
    Not quite. I understand what you are doing with the bottom, the equation is that of a sphere, and therefore you are using another equation to show the bottom is going to 0. But how exactly does that prove the numerator is going to 0 as well?
     
  5. Apr 9, 2009 #4

    Dick

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    If |x|<r and |y|<r and |z|<r, what about |x^3+y^3+z^3|?
     
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