Oliver K

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17 years, 45 days

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These are answers submitted by Oliver K

Hi,

apply the command
combine (%);
to the result and you are very close to what you want. Probably more fine tuning makes it perfect.

restart:
f:=(4*(x-1/2)^3-6*(x-1/2)^2+(x-1/2)+3/2);
p1:=plot(f,x=1/4..1.9,y=0..3,discont=true,colour=blue,style=line,linestyle=dashdot,thickness=2,axis[1]=[tickmarks=[1.9="end"]]);
p2:=plot(2,x=0..2,y=0..3,colour="DarkGreen",style=line,linestyle=dash,thickness=2);
p3:=plot([1.9,t,t=0..2],style=line,linestyle=dash,thickness=2,colour=orange);
plots[display](p1,p2,p3,view=[0..2.1,0..2.5]);

Try to increase the number of points (default=200) in the inspector tab on the right side.

It works here, i tried it with MapleSim 3 and 4. Unfortunately, i cannot see what the custom component does.

Just specify as approximation a starting point for fsolve's iterations,

fsolve(A3,S=1);

edit: sorry for the square root in the pic.

restart:with(plots):
p1:=intersectplot(sqrt(x^2-4*x+4+y^2) = z, z = 2, x = -5 .. 5, y = -5 .. 5, z = -5 .. 5, axes = none, thickness = 2, orientation = [70, 40], scaling = constrained, numpoints = 1000,thickness=3,axes=normal);p2:=plot3d(sqrt(x^2-4*x+4+y^2),x=-6..6,y=-6..6,colour=gray,style=patchnogrid,transparency=0.8);
p3:=implicitplot3d(z=2,x=-6..6,y=-6..6,z=-2..6,style=patchnogrid,transparency=0.9,colour=blue);
display(p1,p2,p3);

Finding most general solutions for a problem in Maple is a task for life (or for true experts).

You could restrict your solutions:

restart:
f:=x->3/(1-exp(1/x));
L:=discont(f(x),x);
reals:=select(x->Im(x)=0,L);

Or use fdiscont

restart:
p:=proc(x,y) if y < 3-x and 0 < x and 0 < y then sin(2*x+2*y) else NULL end if end proc;
plot3d(p, -1 .. 3, -3 .. 3, grid = [50, 50], axes = normal);

Problem with this approach: There are often torn boundaries (the sawtooth-like border in this example) that makes the plot look ugly. A more dense grid does not always really help.

Christopher, I used your code and added numpoints=1000 (looks smooth). You may get irritated in the process of gif export: After being asked for save location and pressing save button, everything gets freezed until the 14MB gif is saved completely, this took me a minute or more, but the gif is ok.

You can also try ?simplify,siderels

 

The x value of the symmetry axe is also an extremum, so you also could use ?extrema for this purpose. Or use completesquare to find x.

Some alternatives you could play with:

a) Write 22=10/9*k and export to LaTex

b) You could put it into quotes: "22=K/.9", rightclick->convert to symbol, export to LaTex

c) Write 22=K/.9, select the input, rightclick->2D math->convert to-> atomic identifier, and export this to LaTex

 

The output of NLPSolve for fmax and fmin is a nested list, what is (fmax-fmin)/fmoy supposed to be ?

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