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

#### maxhersch

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

#### kuruman

Homework Helper
Gold Member
$z(x,y)=ye^{-x}$? Can you think of another one?

#### mathman

$z=\frac{y}{1+x}$.

#### mfb

Mentor
$z=\frac{y}{1+x}$.
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.

#### mathman

$z=\frac{y}{1+x^2}$

mfb

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

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