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?