I need help figuring out how to generate the two graphs of
𝑓(𝑥, 𝑦)=𝑎*𝑠𝑖𝑛(𝑥)𝑒−𝑦^2+ 𝑏𝑐𝑜𝑠(𝑦)*𝑒^−x^2
and
𝑓(𝑥, 𝑦)=𝑎*𝑐𝑜𝑠(sqrt(𝑥^2 + 𝑦^2))+𝑒^−sqrt(𝑥^2+𝑦^2).
I need help figuring out how to generate the two graphs of
𝑓(𝑥, 𝑦)=𝑎*𝑠𝑖𝑛(𝑥)𝑒−𝑦^2+ 𝑏𝑐𝑜𝑠(𝑦)*𝑒^−x^2
and
𝑓(𝑥, 𝑦)=𝑎*𝑐𝑜𝑠(sqrt(𝑥^2 + 𝑦^2))+𝑒^−sqrt(𝑥^2+𝑦^2).
Here is a Asymptote figure for the second 3D graph, with a=2
, b=3
.
PS: The reason I give an answer to the above non-MWE question is twofold. First, that is for welcoming a beginner. Second, I think that function is a nice example in teaching limit of 2 variables functions. At infinity, the function tends to zero, in all direction but x
and y
axes. After all, the figure is eye-caching with high and low mountains along axes. Happy Lunar New Year!
// http://asymptote.ualberta.ca/
usepackage("amsmath");
unitsize(1cm);
size(8cm);
import graph3;
currentprojection=orthographic(4,2,2,zoom=.9);
real a=2,b=3;
real g(pair M) {real x=M.x, y=M.y;
return a*sin(x)*exp(-y^2)+b*cos(y)*exp(-x^2);
}
real t=15;
pair A=(-t,-t), B=(t,t);
surface sg = surface(g,A,B,nx=30,Spline);
draw(sg,surfacepen=yellow,meshpen=purple);
label("$z=ae^{-y^2}\sin x+be^{-x^2}\cos y$",(a+b+10)*Z);
draw(Label("$x$",EndPoint,align=S),O--(t+5)*X,Arrow3);
draw(Label("$y$",EndPoint),O--(t+5)*Y,Arrow3);
draw(Label("$z$",EndPoint),O--(a+b+5)*Z,Arrow3);
I will assume that in the first function, a and b are equal to 1. Here is an example for the first function:
\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}
\addplot3[surf, ]{sin(x)*exp(-y^2)+cos(y)*exp(-x^2)};
\end{axis}
\end{tikzpicture}
\end{document}
For the second one: just change the addplot3 to:
\addplot3[surf,]{cos(sqrt(x^2+y^2))+exp(-sqrt(x^2+y^2)};