# Find $\delta$ for given epsilon in limit question

Given $$f(x,y) = \frac {2x^4-5x^2y^2 + y^5}{(x^2 + y^2)^2} , (x,y) \neq (0,0) ~~\mbox{and} ~~f(x,y) = 0 , (x,y) =(0,0)$$

Find a $$\delta$$ such that $$|f(x,y)-f(0,0)| < 0.01$$ whenever $$\sqrt {x^2+ y^2} < \delta$$

i tried to go into polar coordinates but unable to find it.

There is no such $$\delta$$. Your function is not continuous at $$(0,0)$$, (consider what happens at $$f(x,0)$$ as $$x$$ approaches $$0$$.)
• @Gathdi $\lim_{x\to 0} f(x,0)=2$ so $f(x,0)$ can not get close to $f(0,0)=0$. – Julian Mejia Jun 12 at 3:41