1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Evaluating limits of several variables

  1. Oct 5, 2004 #1
    Hi, in evaluating limits of several variables, is there a general method in approaching it? The plugging in the values method is easy, but the harder limits such as those 0/0 form...is there a general guideline to solving those problems?

    How do I evaulate the following limits? (need tips and hints, not answer :tongue2:)
    [tex]\lim_{\substack{x\rightarrow 0\\y\rightarrow 0}} f(x,y) = \frac{(x-1)^2\ln{x}}{(x-1)^2y^2}[/tex]

    [tex]\lim_{\substack{x\rightarrow 0\\y\rightarrow 0}} f(x,y)=\frac{x^2y}{x^2+y^2}[/tex]

    [tex]\lim_{\substack{x\rightarrow 0\\y\rightarrow 0}} f(x,y)=\frac{x^2+y^2-z^2}{x^2+y^2+z^2}[/tex]

    [tex]\lim_{\substack{x\rightarrow 0\\y\rightarrow 0}} f(x,y)=\frac{4xy}{3y^2-x^2}[/tex]

    Thank you for the help.
  2. jcsd
  3. Oct 5, 2004 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    Firstly, an easy check you must do is to see if the limit does genuinely exist.

    Often, it doesn't for easy reasons, or you find the what the limit out to be in the checking.

    To do this a standard technique is to let x and y tend to zero along some particular path, eg let x=y and tend to zero and then x=2y and let that tend to zero and see fi you get the same answer.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Evaluating limits of several variables
  1. Evaluate the limit (Replies: 10)