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Limit in Two variables.

  1. Oct 8, 2013 #1
    1. The problem statement, all variables and given/known data

    lim (x,y)[itex]\rightarrow[/itex](0,0) f(x,y)=2*x/(x[itex]^{2}[/itex] + x +y[itex]^{2}[/itex])

    2. Relevant equations

    used different paths like y=k*x ,where k is a constant and y=k*x^2

    3. The attempt at a solution
    Got an answer 2 but solution says does not exist. Can anybody convince me that why limit does not exist,without using polar form.

    I am currently studying in 1st year of college.
  2. jcsd
  3. Oct 8, 2013 #2


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    The problem with the paths you chose is that there is one direction you are unable to represent with a finite k. What direction do you think that would be?
  4. Oct 11, 2013 #3
    oh got it thanks man. its the y axis!! The limit comes out to be zero if i put x=1. Thanks!
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