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!

Homework Help: Does the limit exist or not?

  1. Feb 18, 2016 #1
    1. The problem statement, all variables and given/known data
    Prove that

    lim (x,y,z)→(0,0,0) 2xz/(x²+y²+z²) = 0

    2. Relevant equations
    My teacher wants me to show this using epsilon delta, so

    0<√(x²+y²+z²)<∂ ⇒ |f(x,y,z) - 0| < ε

    3. The attempt at a solution
    The limit does not exist apparently.. when you approach the limit along different paths you get different answers.. say, along (t,0,t) gives 1 while along (0,0,t) gives 0. Did my professor make a mistake in this assignment, or does the limit actually exist and I'm missing something?
  2. jcsd
  3. Feb 18, 2016 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You're right. Your professor made a mistake.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted