Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

$f(x,y)=\frac{xy^3}{x^2 + 4y^2}$,

$(x,y)$ not eaqual to $(0,0)$;

use $\epsilon-\delta$ definition to show that $f(x,y)$ tends to $(0,0)$.

I'm unsure how to deal with fractions for, $\epsilon-\delta$ proof... could applying the proof separately for numerator and denominator; then later combining them help?

share|cite|improve this question
up vote 0 down vote accepted

$\mathbb x^2 + 4y^2\geq 4xy$ applying AM $\geq$ GM then $ f(x.y) \leq \frac{y^2}{4} $ from there you can get the $\epsilon-\delta $ proof

share|cite|improve this answer
so i essentially apply epsilon-delta to y^2/4. meaning the answer is delta< (4*epsilon)^0.5 – redrum Oct 23 '12 at 13:23
oh AM = arithmetic mean, and GM = geometric mean. Also your initial equation doesn't really remind me of how it links to AM or GM. – redrum Oct 23 '12 at 13:40
yes AM = arithmetic mean, and GM = geometric mean from this (a+b)/2 >= sqrt(ab) take a=x^2 (>=0) and b= 4y^2(>=0) – jim Oct 23 '12 at 14:10

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.