Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Nov 9, 2018 #1
    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. jcsd
  3. Nov 9, 2018 #2

    kuruman

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    ##z(x,y)=ye^{-x}##? Can you think of another one?
     
  4. Nov 9, 2018 #3

    mathman

    User Avatar
    Science Advisor

    ##z=\frac{y}{1+x}##.
     
  5. Nov 9, 2018 #4

    mfb

    User Avatar
    2017 Award

    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.
     
  6. Nov 10, 2018 #5

    mathman

    User Avatar
    Science Advisor

    ##z=\frac{y}{1+x^2}##
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted