Show that the limit does not exist $\lim_{(x, y) \to (0,0)}\frac{5x^2}{x^2 + y^2}$

Question

attempt:

let $y = 0$

$\lim_{x \to 0} \frac{5x^2}{x^2 + 0^2} = 5$

let $x = 0$

$\lim_{y \to 0} \frac{5(0)^2}{y^2} = 0$

$5 \neq 0$, therefore two different values, limit does not exist

right?

The technique you've used in this question is exactly the same as the technique from your question yesterday, your question four hours ago, and likewise 12 minutes ago. Perhaps you could ask about a concept you're not sure of, rather than near-duplicated computations. — , Oct 19 '18 at 02:44

score 1 · Accepted Answer · answered Oct 19 '18 at 02:44

1

Yes, your proof is complete and you have explained your work clearly.

answered Oct 19 '18 at 02:44

1 Answers1