- #1
Mindstein
- 14
- 0
Homework Statement
Evaluate the limit of the function f(x,y) = [tex]\frac{y^3}{x^2+y^2}[/tex]
Homework Equations
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*sin2(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.