http://calc3.askbot.com/questions/Open source question and answer forum written in Python and DjangoenCopyright Askbot, 2010-2011.Wed, 16 Jul 2014 20:48:15 -0500http://calc3.askbot.com/question/109/more-matching-of-groovy-plots-and-functions/So I'm having a hard time determining the difference between plots $I$ and $II$. I know that they are both either $f(x,y)=\cos(x^{2}+y^{2})$ or $f(x,y)=e^{-(x^{2}+y^{2})}$. But I can't think of a way to tell them apart. *Comment*: They both have circular symmetry but only one has some sort of wavy behavior.SpaceManSpiffWed, 16 Jul 2014 20:48:15 -0500http://calc3.askbot.com/question/109/http://calc3.askbot.com/question/75/yesterdays-worksheet-contour-problems/On the worksheet we did yesterday, the second two questions asked to sketch the contour diagrams of $f(x,y) = 4x^2 + 9y^2$ and $f(x,y) = 4x^2 - 9y^2$. For the first one, during class me and my group figured out the contours by setting the function equal to a constant, and then seeing that we had an equation for an ellipse, getting a diagram of several ellipses wider in the $x$ axis than the $y$ axis. Is this the correct approach? If it is, is there is a way to determine the contours for more complicated functions where we might not recognize immediately that it gives the equation for a simple shape?DylanWed, 09 Jul 2014 22:33:41 -0500http://calc3.askbot.com/question/75/