Multivariate Limit

  • Thread starter trap101
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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?
 

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  • #2
Ray Vickson
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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?

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


Using L'Hospital's rule, would I essentially be treating "y" as a constant?
 
  • #4
Dick
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Using L'Hospital's rule, would I essentially be treating "y" as a constant?

Yes!
 

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