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Function, using two-path test, finding limits

  1. Apr 29, 2010 #1
    f(x,y)=(x)/ (1-y2), y does not equal 1 or -1

    Is it possible to define a new function g(x,y) that is defined and continuous for all (x,y) in R2, and such that g(x,y)=f(x,y) for all (x,y) in the domain of f? If so, find such a function. If not, explain why.


    I really don't know where to begin...
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 1, 2010 #2
    For the existence of such g it is necesarry that lim (x->x0, y->1) f(x,y)=A(x0,1) exist and depend only on x0 (and not on the path). But in our case it does not hold:

    Calculate the limit for x0=0 for two different paths:
    1. y=x+1 (x->0)
    2. y=2x+1 (x->0)

    You wont get the same result, so such g does NOT exist.
     
  4. Apr 18, 2012 #3
    how do i choose the equations of lines c and d,to find limits along when finding limits by two parts
     
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