I'm working on displayind*g the regions where a specific condition between two functions. As an example I want to color or highlight in a way or another the areas where let's say where x/ f(x)<g(x)< p="">
f(x)=sin(2*x + 3)
g(x)=2*cos(2*x + 2)
plot([f(x),g(x)],[x,-pi,pi])How can I approach that ? Thx for any kind of hint.
What about
f(x)=sin(2*x + 3)
g(x)=2*cos(2*x + 2)
h=g(x)-f(x)
x0=find_root(h, -3,-1)
x1=find_root(h, -1,0)
p1=plot([f(x),g(x)],[x,x0,x1],fill=True,fillcolor='lightgrey')
p2=plot([f(x),g(x)],[x,x0+pi,x1+pi],fill=True,fillcolor='lightgrey')
p=plot([f(x),g(x)],[x,-pi,pi])
p+p1+p2Excellent ! That's a very nice starting point for me. In fact we cannot identify where (in this example) f(x)=g(x) therefore a need to tell where to look at. May be making a loop over small intervals could work in simple case. This is by no mean a general solution by def. Thx a lot. appreciated !
Examples like sin(1/x), cos(1/x) are overwhelming.
To complement the answer by @achrzesz, let us point out two additional approaches to fill exactly the region between the curves y=f(x) and y=g(x) where f(x)≤g(x), with x in a given interval [a,b], that is, the region
{(x,y)∈R2∣a≤x≤b, f(x)≤y≤g(x)}.
First method:
f(x) = sin(2*x+3)
g(x) = 2*cos(2*x+2)
pf = plot(f(x), (x,-3,3), color="red", fill=max_symbolic(f(x),g(x)),
fillcolor="lightgreen")
pg = plot(g(x), (x,-3,3), color="blue")
show(pf+pg)Second method:
var("x,y")
p = plot([f(x),g(x)], (x,-3,3), color=["red","blue"])
r = region_plot([f(x)<y, y<g(x)], (x,-3,3), (y,-2,2),
incol="lightgreen", plot_points=[100,100])
show(r+p)See this SageMath Cell
Asked: 2 years ago
Seen: 317 times
Last updated: Jan 04 '23
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