Trying to press on through Epsilon-Delta proofs of limits (for more than one variable) and yet there's only one example I've found thus far of even a multi-variable Epsilon-Delta proof.(adsbygoogle = window.adsbygoogle || []).push({});

Would it be possible for someone to solve the Epsilon-Delta proof of the limit:

(xy^2)/(x^2+y^2). Note: The limit does *not* exist... along straight-line paths the limit is 0, yet on the x=y^2 parabola the limit is 1/2.

x=y^2

IE: (y^2)y^2/(y^2)^2+y^4 = y^4/2y^4 = 1/2.

Profs always say Epsilon-Delta proofs are among the hardest things to get in math... go figure! You try and get examples and its always the same 3 recycled over and over, and all are examples of limits which exist. Most are even polynomial aswell, which makes it super-easy. (Except you never see Polynomial proofs on exams, no they must give you rationals)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Epsilon-Delta Proofs of Limits

**Physics Forums | Science Articles, Homework Help, Discussion**