1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Limit as 9x,y) approaches (0,0)

  1. Oct 19, 2009 #1
    1. The problem statement, all variables and given/known data

    Justify if the limit of the following function exists as (x,y) approaches (0,0). If it exists find the limit using the squeezing technique.
    f(x,y)=(exy-1)/(x2+y2)

    2. Relevant equations



    3. The attempt at a solution

    I found the limit of f(x,0) to approach 0
    I found the limit of f(0,y) to approach 0
    Since this is insufficient I found the limit of f(x,x)=(ex2-1)/2x2

    Thanks for any help.
     
  2. jcsd
  3. Oct 19, 2009 #2

    lanedance

    User Avatar
    Homework Helper

    why not extend the evaluation to all linear trajectories towards the origin given by y = cx, for some real c

    then evaluate the limit of
    (lim x->0) g(x) = f(x,cx)
    if it is indeterminate, try using L'hopitals rule

    does the limit depend on c?
     
  4. Oct 20, 2009 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Unfortunately, even if the limit, as you approach (0,0) along every line is the same, it might still be different for some curve- and so the limit might not exist.
     
  5. Oct 20, 2009 #4

    lanedance

    User Avatar
    Homework Helper

    ok, but if you can show that dependent on the line of approach, the result differs, you have shown the limit does not exist
     
  6. Nov 2, 2009 #5
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Limit as 9x,y) approaches (0,0)
Loading...