(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate the limit of the function f(x,y) = [tex]\frac{y^3}{x^2+y^2}[/tex]

2. Relevant equations

3. The attempt at a solution

Well, I approached this problem using the multiple-path method and found the following:

[tex]\stackrel{lim}{x\rightarrow 0} [/tex] [tex]\frac{y^3}{x^2+y^2}[/tex] = y

[tex]\stackrel{lim}{y\rightarrow 0} [/tex] [tex]\frac{y^3}{x^2+y^2}[/tex] = 0

and am having trouble interpreting these results. I tried doing a polar substitution and found that:

[tex]\stackrel{lim}{r\rightarrow 0} [/tex] [tex]\frac{y^3}{x^2+y^2}[/tex] = y*sin^{2}(theta)

My calculus book is very short on the topic, I am pretty much left in the dark. Please bring me into the light. haha.

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# Homework Help: Limit of a Function of Two Variables

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