- #1
andrassy
- 45
- 0
Homework Statement
I need to evaluate this limit by converting to polar coordinates:lim (x,y) -> (0,0) of (x^2 + xy + y^2) / x^2 + y^2
Homework Equations
x = rcos(theta), y = rsin(theta)The Attempt at a Solution
So switching to polar I get:[(rcos(theta))^2 + rcos(theta)rsin(theta) + (rsin(theta))^2] / (rcos(theta))^2 + (rsin(theta))^2
By pulling out the r^2 from the the top of the equation and the bottom of the equation, they can cancel. Then the denominator is cos(theta)^2 + sin(theta)^2 which equals 1.
So we get the limit of cos(theta)^2 + cos(theta)sin(theta) + sin(theta)^2 but I don't know what to do from here because this is the limit as r goes to 0 and there is no r?
I'm kinda stuck here...what can I do? We didn't really get taught this so I could be missing something simple.
Thanks!