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Limits with multi-variables

  1. Mar 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the limit for x = 0 y= 0 for sin(x^2+y^2)/x^2+y^2

    2. Relevant equations

    I'm trying to use the squeeze method using the inequality |ab| <= 1/2(a^2+b^2)

    3. The attempt at a solution

    Is there a way I can convert sin(x^2+y^2) into absolute value |ab|

    so I can get |ab| <= (1/2(x^2+y^2))/x^2+y^2

    or should I use a different inequality?
  2. jcsd
  3. Mar 25, 2009 #2


    Staff: Mentor

    I don't think the approach you're attempting will do you any good. How about converting to polar coordinates? Then you're looking at the limit as r approaches zero.
  4. Mar 25, 2009 #3

    should I find the limit r -> 0 of sin(R^2)/R^2

    = 1

  5. Mar 25, 2009 #4


    Staff: Mentor

    That's what it looks like to me.
  6. Mar 25, 2009 #5
    Thanks alot!
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