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Limit of multi variable

  1. Mar 18, 2013 #1
    1. The problem statement, all variables and given/known data
    lim(x,y)-(1,0) ln((1+y^2)/(x^2+xy))


    2. Relevant equations



    3. The attempt at a solution
    if i just substitude x and y i get ln (1)= 0 so is the limit 0?
     
  2. jcsd
  3. Mar 18, 2013 #2

    tiny-tim

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    hi munkhuu1! :smile:
    almost

    the limit of a product (or quotient) is the product (or quotient) of the limits if they exist,

    so you also need to point out that the two limits exist :wink:
     
  4. Mar 18, 2013 #3
    thank you, and so do i need to see if df/dx and df/dy exists? or something else?
     
  5. Mar 18, 2013 #4

    tiny-tim

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    (in some cases, that might not be enough!)

    no, just point out that it's obvious that the limits of 1 +y2 and of x2 + xy exist :wink:
     
  6. Mar 18, 2013 #5
    thank you. :approve:
     
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