Recent content by cereeal

If anyone else could help it would be greatly appreciated. Would the previous arctan(y/x) function be the answer? Either way, I also do know where to start.

Nevermind, I agree with that modtor. I'm not getting any progress on (h) though.

What parametrization did you use for C? I tried thinking about what Dick said a few posts ago and it seems the line integral increases the more turns you go around a path so wouldn't that mean all values are possible? And for the last question, because arctan(y/x) isn't defined on the y-axis...

Or use squeeze method: |xln(x^2+y^2)| \leq f(x,y) \leq 2|xln(x)|

Thanks, couldn't get those integrals working for some reason. And that's true, I don't know why I didn't think of using the same application on the closed shape not at the origin, I was stuck on using the inner circle. So for my last question would I still just be applying Green's theorem to it?

For the Green's Theorem I made an arbitrary counterclockwise circle (C') within the enclosed region (D). This gave me: \int _{C} P dx + Q dy + \int_{-C'} P dx + Q dy = \int \int_{D} (\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}) dA = 0 Therefor the two integrals on the left...

We are given a vector field: F=\frac{-y}{x^2+y^2} , \frac{x}{x^2+y^2} Then asked if F is conservative on R2 \ (0,0). I just solved the partial derivatives of each part of the vector field and they did indeed equal each other, but I don't under stand what the "\(0,0)" part means. We are then...