Show-that-lim-x-y-0-0-3-x-2-2y-2-does-not-exist-

Question Number 69319 by Joel122 last updated on 22/Sep/19

Show that

\lim_{(x, y) \to (0, 0)} \frac{3}{x^{2} + 2 y^{2}}

does not exist

Commented by Joel122 last updated on 22/Sep/19

I have approached (0, 0) along x - axis, y - axis,

y = x, y = x^{2}, y = \sqrt{x} and it give same answer + \infty

So, why the limit {doesn}^{'} t exist ? Should I

try using different approach ?

Commented by MJS last updated on 22/Sep/19

\lim = \pm \infty means it {doesn}^{'} t exist because

\pm \infty \notin R

Commented by prof Abdo imad last updated on 23/Sep/19

x = r c o s θ a n d y = \frac{r}{\sqrt{2}} s i n θ (x, y) \to (0, 0) \Rightarrow r \to 0

a n d {l i m}_{(x, y) \to (0, 0)} \frac{3}{x^{2} + 2 y^{2}} = {l i m}_{r \to 0} \frac{3}{r^{2}} = + \infty

s o t h e l i m i t i s i n f i n i t e

Commented by Joel122 last updated on 23/Sep/19

t h a n k y o u S i r

Facebook Tweet Pin