http://calc3.askbot.com/questions/Open source question and answer forum written in Python and DjangoenCopyright Askbot, 2010-2011.Wed, 16 Jul 2014 22:18:51 -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.Wed, 16 Jul 2014 20:48:15 -0500http://calc3.askbot.com/question/109/more-matching-of-groovy-plots-and-functions/http://calc3.askbot.com/question/109/more-matching-of-groovy-plots-and-functions/?answer=114#post-id-114I'm not sure about how solid this reasoning is, but I sort of based my answer on how I know $e^{-x^2}$ behaves. This type of function has a high value at one spot and a low value everywhere else; adding $y^2$ to the exponent should only extend this to another dimension. Plot II looks like it peaks in one spot and is small everywhere else, so I would pick it to be the plot of $e^{-(x^2+y^2)}$. In general I sort of expect $e^{-(junk)^2}$ to behave like this since we use these functions so often to represent peak values in one area with minimal values in others. I've also noticed that on our sheets, a lot of the plots that look like isolated hills and holes are complicated combinations and variations of this type of function.Wed, 16 Jul 2014 22:18:51 -0500http://calc3.askbot.com/question/109/more-matching-of-groovy-plots-and-functions/?answer=114#post-id-114