Take the 2-minute tour ×
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.

How to prove $\lim_{(x,y)\to (0,0)} f(x,y)=\frac{|x|^\alpha y^4}{x^2+y^4}$ for all $\alpha>0$?

I think in order to prove this limit exists, I should the value is all the same from different direction. How to prove at here?

share|improve this question
    
$f=|x|^{\alpha} - \dfrac{|x|^{2+\alpha}}{x^2+y^4}$ consider limits for both. $|\dfrac{|x|^{2+\alpha}}{x^2+y^4}|\le \dfrac{|x|^{2+\alpha}}{x^2}$ –  Yimin Feb 22 '13 at 4:21
2  
Note $y^4/(x^2+y^4)<1$ –  Maesumi Feb 22 '13 at 4:46

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.