1
$\begingroup$

I'm trying to find $2$ paths through $(0,0)$ to show that $\lim_{(x,y) \to (0,0)}\dfrac{xy^2}{x^2 + y^4}$ does not exist.

I only manage to use path $y=x$ but can't find second one. Any thoughts on which path to choose to show that this limit doesn't exist? Thanks!

$\endgroup$
  • $\begingroup$ Try $x=t^2$, $y=t$. $\endgroup$ – user137731 Jul 8 '16 at 1:06
  • $\begingroup$ Thanks for the suggestion! $\endgroup$ – Sandra Jul 8 '16 at 1:24
  • $\begingroup$ Try $y=0$ and $x=y^2$. $\endgroup$ – user84413 Jul 8 '16 at 4:57
1
$\begingroup$

Choose $y=x$ and $y=\sqrt{x}$.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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