Community RSS Feed https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions in tag Calculus sorted by active Splitting a point with Mathematica and MathTensor: a Mathematica memoir https://community.wolfram.com/groups/-/m/t/2552454 &amp;[Wolfram Notebook] : https://www.wolframcloud.com/obj/ea30426e-76b3-4839-8405-2f96cea4879a Steven Christensen 2022-06-17T22:21:20Z Mathematica-3DPlots and Laurent series of Multivariable functions https://community.wolfram.com/groups/-/m/t/2560605 Dear all, I hope you are doing well. **Previously, I have tried to submit this question, however, I forgot to include my attempts which now I do so. Attached below, you may find my notebook with my doubts. It should be remarked that I have also read Mathematica&#039;s documentation. However, this latter did not help me with the Taylor and Laurent series expansion of multivariable functions.** With that said, suppose that we have the following multivariable function $\displaystyle \psi(x,y)=\frac{-((2 (132 + 56 x^4 - 382 y + 394 y^2 - 171 y^3 + 26 y^4 + 6 x^3 (-47 + 31 y) + x^2 (608 - 782 y + 240 y^2) + x (-602 + 1130 y - 716 y^2 + 153 y^3)))}{((16 + 4 x^2 + 8 x (-2 + y) - 16 y + 5 y^2)^2 (5 x^2 + (3 - 2 y)^2 + x (-6 + 4 y))^2))}$ Based on the above, I ask the following questions: 1. How may I construct a 3D plot of $\psi(x,y)$ so that positive and negative values are represented by red and blue colors, respectively? As one can readily see from the notebook attached below, I have considered the ColorFunction command to represent the positive and negative values of $\psi(x,y)$. However, I am not quite sure whether this is correct. As we may observe, $\psi(x,y)$ is a negative function. Hence, should not we observe a predominantly blue color in the 3D plot of $\psi$? 2. Is there a way to determine whether or not $\psi(x,y)$ is symmetric using Mathematica? 3. I have read Mathematica&#039;s documentation, however, I did not find a proper approach to performing series expansion of multivariable functions like $\psi$. Consequently, How may one perform the Taylor or Laurent series of this function in the neighborhood of the point $\displaystyle (x,y)=(2,1)$ through Mathematica? Thanks once more and I look forward to hearing from you. Vinícius Hopkins 2022-06-29T22:56:38Z What value of x splits the area under the curve in half? https://community.wolfram.com/groups/-/m/t/2562035 How do I calculate at what point on the x axis half the area under the curve is to the right of x, and half to the left? &amp;[Wolfram Notebook] : https://www.wolframcloud.com/obj/418c35e2-125c-46ac-9140-11dbbf18a6b8 Jonathan Wooldridge 2022-07-01T18:30:28Z