Oliver K

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17 years, 36 days

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These are answers submitted by Oliver K

 

f:=(1-k)*x^2+k*sin(x);
plots[animate](plot, [f,x=0..10,y=-1..5],k=0..1,frames=50);

 

Regarding your x^2->x^3 morphing, remember that something like x^(5/2) is complex valued for negative x, how do you want to plot this ?

Do you mean something like this ?

plots[animate](plot, [x^i,x=0..10], i=2..3);

This is one case where a nicely formatted task template would be actually useful.

Ok let me tell you where i came from. I'm interested in finding closed form expressions for the n-th derivative of a function (see Whats new->Symbolics->symbolic order differentiation). This has been enhanced in Maple 14, but it still sucks a bit, so i'm looking for ways to improve it.For example, diff(cos(x)^2,x$n) does not work, but the equivalent diff(1/2+1/2*cos(2*x),x$n) does. For function compositions, there is Bruno's formula to give at least a sum representation of the n times differentation, see

http://en.wikipedia.org/wiki/Fa%C3%A0_di_Bruno%27s_formula

One variant of this formula requires Bell Polynomials of the second kind. But if Maple does not have this, i better use another variant.

With this formula, Maple would return something for diff(sin(cos(x)),x$n), which remains unevaluated right now.

Thanks for the hint, it works now.

restart:with(combinat):
L:=permute([x,x,x,x,x,0,0,0,0]): # if 0 starts then L:=permute([x,x,x,x,0,0,0,0,0]):
seq(Matrix(3,L[i]),i=1..5);

Of course, this is without considering win conditions.

I thought i could use this show solution steps to trace what's up with this wrong calculated limit:

restart:with(Student[Calculus1]):
Limit(x^(Pi/2-arctan(x)),x=infinity);

Unfortunately, Maple hangs here.

s:=[t=2.,i1(t)=0.929532062300405666e-1,s1(t)=.907046793769959448];

s[2];rhs(s[2]);

 

Additionally, in Maple 14 the PDETools Package has a unified Solve command (notice the upper case S), which has an option called independentof. It provides an extended solve/identity capability.

 

solve(identity(a*cos(x)+b*sin(x) = c*cos(x+d), x), [c, d]);

i see,thanks!

Do you have an example?

I would start with ?phaseportrait

Try SurfacePlot from the Statistics Package

With Maple 13 and Win7 reformatting+reinstall is no problem as long as your hostid remains the same (change of mainboard could be a problem, for example). Under Windows, until Maple 11 only the disk serial number of the hard disk was used to identify the hardware. A reformat of the hd can change this id and Maplesoft's activation server cannot match locally stored data and the recieved data during activation. Since Maple 12, additionally the MAC adress of the ethernet card is checked, so there should be no problem here. 

Check the plotting guide, especially Dynamical Systems Package for such tasks. If needed, use plots[display] to combine plots.

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