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

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

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?

• yes ${}{}{}{}{}$ – TomGrubb Oct 19 '18 at 2:43
• Yes, that's right. – saulspatz Oct 19 '18 at 2:43
• 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. – user296602 Oct 19 '18 at 2:44
• – user296602 Oct 19 '18 at 2:45
• Tree.All is well. – Peter Szilas Oct 19 '18 at 8:51