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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

    vela

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    You're right. Your professor made a mistake.
     
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