I want to define a function knowing only it's limits

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  • Thread starter maxhersch
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  • #1
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This is a random problem I am trying to figure out. The context doesn't matter.

I wish to define a function z(x, y) based on the following limits:

1. lim z (x→∞) = 0
2. lim z (x→0) = y
3. lim z (y→∞) = ∞
4. lim z (y→0) = 0
 

Answers and Replies

  • #2
kuruman
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##z(x,y)=ye^{-x}##? Can you think of another one?
 
  • #3
mathman
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##z=\frac{y}{1+x}##.
 
  • #4
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##z=\frac{y}{1+x}##.
For ##x<-1## this doesn't have the right behavior for ##y \to \infty##. If we require x,y to be non-negative it works.
 
  • #5
mathman
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##z=\frac{y}{1+x^2}##
 
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