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

1. Nov 9, 2018

### 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

2. Nov 9, 2018

### kuruman

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

3. Nov 9, 2018

### mathman

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

4. Nov 9, 2018

### Staff: Mentor

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. Nov 10, 2018

### mathman

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