Question

%2B%20y%5E2%29%20" id="TexFormula1" title=" \lim_{(x,y) \to \ (0,0)} (x^4 +y^3)/(x^4 + y^2) " alt=" \lim_{(x,y) \to \ (0,0)} (x^4 +y^3)/(x^4 + y^2) " align="absmiddle" class="latex-formula">

Answer 1

If $x=0$, you have

$\displaystyle\lim_{y\to0}\frac{y^3}{y^2}=\lim_{y\to0}y=0$

But if $y=0$, you have

$\displaystyle\lim_{x\to0}\frac{x^4}{x^4}=\lim_{x\to0}1=1$

So the limit does not exist.