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Functions of 3 Variables - Limits

  1. Feb 12, 2008 #1
    1. The problem statement, all variables and given/known data
    I am to find the limit if it exists as (x,y,z) -> (0,0,0) of
    (x^2+2y^2+3z^2)/(x^2+y^2+z^2)
    If it doesn't exist, show that it does not exist.

    3. The attempt at a solution
    I know how to do with for functions of two variables, to approach on the x axis, and y axis, and maybe even occasionally on y=x or other lines to find out if the limit exists, but I haven't been able to find out how to apply this to 3 variables.

    I'm not sure if i am to take f(0,0,z), f(0,y,0), and f(x,0,0) and see if i can draw conclusions from here, or alternatively, f(0,y,z), f(x,0,z), f(x,y,0).

    Thank you. (this is for a calculus 3 course, undergraduate)
     
  2. jcsd
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