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

• B
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