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How do I find a limit with two variables?

  1. Mar 2, 2014 #1
    How do I find a limit with two variables???

    1. The problem statement, all variables and given/known data

    lim(x->0)((1+ax)^(1/3)/(xln(1+x))-(arctan(bx)/(x^3))

    http://www.wolframalpha.com/input/?i=lim%28x-%3E0%29%28%281%2Bax%29^%281%2F3%29%2F%28xln%281%2Bx%29%29-%28arctan%28bx%29%2F%28x^3%29%29



    I understand that since the denominator x^3ln(1+x)---> 0 then the counter must also go to zero.

    But what I do not understand is that since the counter has TWO variables, I always get a function of those two, instead of a solution of each.

    The answer in WA isn't even sensible either


    UPDATE:

    I have figured some of it, found out that

    a= -3/2 and b= 1

    Now how do I find the limit?
     
    Last edited: Mar 2, 2014
  2. jcsd
  3. Mar 2, 2014 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    What I don't understand is what the expression you are trying to find the limit of is. Your parentheses don't match up. Is it ##\frac{(1+ax)^{1/3}}{xln(1+x)-\frac{arctan(bx)}{x^3}}##? Or ##\frac{(1+ax)^{1/3}}{xln(1+x)}-\frac{arctan(bx)}{x^3}##? Or something else?
     
  4. Mar 3, 2014 #3
    it is:

    ##\frac{(1+ax)^{1/3}}{xln(1+x)}-\frac{arctan(bx)}{x^3}##

    And i have solved it now
     
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