Proof of Limit: $\varepsilon$-$\delta$ Definition

[kidia]

Please I need help on this one.

Use the $$($$ $$\varepsilon$$ ,$$\delta$$ $$)$$ definition of limit to prove that

lim $$($$x+y/$$x^2$$+$$y^2$$+1$$)$$=0
(x,y)$$\rightarrow$$(0,0)

 

[Hurkyl]

Well, what have you done on this so far? Do you know of any similar problems that you do know how to do?

By the way, I'm pretty sure you meant (x+y)/(x²+y²+1), not x+y/x²+y²+1.

 

[kidia]

No Hurkyl,I haven't done this kind of limit help me.And it is

lim $$($$x+y/$$x^2$$+$$y^2$$+1$$)$$=0
(x,y)$$\rightarrow$$(0,0)