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

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The forum discussion focuses on proving the limit of the function (x+y)/(x²+y²+1) as (x,y) approaches (0,0) using the ε-δ definition of limits. The correct interpretation of the limit is emphasized, clarifying that the expression should be (x+y)/(x²+y²+1). The participants highlight the necessity of understanding the ε-δ framework to approach this proof effectively.

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kidia
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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)
 
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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.
 
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)
 

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