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Multivariate Limit

  1. May 24, 2013 #1
    So I figured out the solution to lim (x,y)-->(0,y) of Sin(xy)/x, but I figured it out by looking at a solution. I wanted to understand though why with respect to the above limit how Sin(xy)/x = y?

    How do you separate the xy in the numerator?
     
  2. jcsd
  3. May 24, 2013 #2

    Ray Vickson

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    Use l'Hospitals's rule, or else look at the behavior of ##\sin \theta## for small ##|\theta|##.
     
  4. May 24, 2013 #3

    Using L'Hospital's rule, would I essentially be treating "y" as a constant?
     
  5. May 24, 2013 #4

    Dick

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    Yes!
     
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