I am doing a Calculus assignment and I can't find the commands for certain things.

1.Given the function f(x) = ((x+1)^2) / (1+x^2)

i) The domain of continuity of f(x)

ii) The intervals of increase and decrease of f(x) by using test points.

2. Use the IVT to prove existence of a root to the equation x^3 +10x^2 -100x +50=0 in the interval [-20,10]. Use again the IVT to show that there is a 1st root in [-17,-15], a 2nd toot in [0,1] and a 3rd root in [ 5,6]. Find or approximate those roots with Maple. (the bolded is what I need help).

I'm have used a program to find the roots of a function 

f:=x*cos(x)-sin(x)*sin(x/1000);
/ 1 \
x cos(x) - sin(x) sin|---- x|
\1000 /

x_max:=50; x_min:=-50; step:=2; i_max:=(x_max-x_min)/step;
50
-50
2
50

j:=1:
for i from 0 to i_max by 1 do
x0:=x_min+i*step;
x[j]:=fsolve(f=0,x=x0);
j:=j+1;
end:

and my output was of the form of multiple "potential" roots and a bunch of which are the same. So I tried to get rid of the ones which were the same before actually finding the ones which ARE roots. To do that I done....

j := 1; for j to 50 do if x[j]-x[j+1] = 0 then ignore(x[j]) else print(x[j]) end if end do:

and it got rid of the ones which are of the above form but some roots are the same and seperated by more than 1 ... i.e x[ j ]= x[j + 2] or some other number. 

Basically I am trying to generalise the above for loop for all "numbers" instead of 1 but when I try some things the for loop doesnt like it. 

Any help would be good!

Hi,

I am working on a Windows machine. In older Maple versions, decreasing the font size for the screen display (via zoom factor) also decreased the font size for the printout. But now the printout comes with a pretty large font size and does not change when using the zoom factor. It practically makes no sense anymore to print. How can I decrease the fonts for the printout to my liking?

Thanks.

heide

hi.please see attached file below and help me

Error, (in solve) cannot solve expressions with diff(diff(diff(f4(x), x), x), x) for diff(diff(f4(x), x), x)

thanks..error.mw

If for example I type :

It gives out this :

I want dsolve to know I'm using real numbers so it gives out something like :

I tried some assumptions and stuff like assume(a,real), but I didn't manage to figure it out.

If that matters, I'm using Maple 18 student.

EDIT : I know dsolve is not necessary for this particular example, but I want to know if it's possible with dsolve or maybe an other tool that can handle ODE.

Thank you in advance !

Hello altogether,

I want to plot the numerical result of an ODE, which seems to be pretty simple at first sight, but the difficulty is that the boundaries are depending on the solution.

The following pseudo-code describes what I want to have, but it doesn't work. This code fills the RAM pretty fast and you will have to kill the process.

Free-boundary_prob.mw

Is it possible to calculate a solution to this problem numerically (or even analytically) and if yes, how?

Since I am new here, I am sorry for any bad-to-read maple code or any noob errors I have made. I would be very thankful, for any response and help.

Greetings

butterflyfart

Hello.

When I input an expression such as 3*(2*x-1)(x+1) > 0 into a Maple worksheet, Maple outputs this:

0 < 6*x(x+1)-3

(sorry, the formatter doesn't work for some reason).

I was wondering by which rules Maple determines to output that instead of, for example,

0 < 3(2*x^2+x-1)

or

0 < 6*x^2+3x-3

Also, Maple can't seem to be able to solve the inequality. It gives the following error to the command:

solve( { 3*(2*x-1)(1+x) > 0 } );

Error, (in solve) cannot solve for an unknown function with other operations in its arguments

So, I was wondering, is there a way to force Maple to output either in the most factorized form (which should be what I gave it as input) or in the least factorized form (that is, multiply it all)?

And, of course, why can't I solve the inequality with Maple?

I am trying to solve system of partial differential equation, but i got some trouble. This is system of heat equations

Here are the equations:

restart;with(PDEtools):
U1 := diff_table(u1(x,t)):
pde[1] := (1/kappa1)*U1[t]=U1[x,x];

bc[1]:=u1(-L, t)=V;

U2 := diff_table(u2(x,t)):
pde[2] := (1/kappa2)*U2[t]=U2[x,x];

bc[2]:=u2(a, t)=0;

sys:=[pde[1],bc[1],pde[2],bc[2], u1(x=0,t)=u2(x=0,t), 

D[2](u1)(x,0)=D[2](u2)(x,0)

]

pdsolve(sys);

a and L is arbitrary constanta

anyone can help? The last boundary conditions I mean du1/dx=du2/dx at x=0

How can i solve this problem? 

Dear all,


I'm having trouble defining a Maple procedure containing for loops. I have one outer for loop which I terminate at the end and two separate for loops of which the first one get's terminated before the second one starts. Nethertheless Maple complains, that my outer loop doesn't get terminated and points to to a point before the second inner for loop starts. I based this procedure on a procedure I defined in another worksheet and the latter one is working just fine, although the structure ist the same in both procedures. As far as I can see, the structure is

for n from 0 to T do
for i from 1 to J do
....
end do;
for i from J-2 to 1 by -1 do
end do;

end do;

I have several if statements in the procedure, too, but as far as I can see, everything is terminated fine. Perhaps there is something else wrong with my procedure and I'm just getting a strange error? I would really appreciateit, if somebody could take a short look at the problem. Since the procedure takes up several pages I'm uploading my Maple work sheet. The relevant procedure is the one defined just after the red comment "#  actual code" which is about 60% through the work sheet.

Thank you all.

BD_collapse_2.mw.

Hi,

Ive been trying to solve critical points for maple but i keep getting this werid equation:

(1/7)*RootOf(tan(_Z)^2+4*_Z*tan(_Z)+4*_Z^2+28*tan(_Z)-140*_Z-1176)+1+(1/14)*tan(RootOf(tan(_Z)^2+4*_Z*tan(_Z)+4*_Z^2+28*tan(_Z)-140*_Z-1176)).

What I have typed

f:=x->(7-x)*sin(x^2-7);

f1:=D(f);

When I try putting:

solve(f1(x)=0);

I get that werid equation

can maple 18 install in mobile phone Lumia 950?

hi.i have problem for dsolve equation.please help me again

thanks alotequation.mw

I have this two matrices

and

and I want to check that their are the same. I have tried

but it says it false. It should say that is true, because - I think- this two matrices are the same.

Does anyone know what is wrong?

Many thanks

I want to compute some matrix multiplications and i need this expression to be 1 always, i.e,

x^2+y^2+z^2+w^2=1

for every calculation I do.

I have tried x^2+y^2+z^2+w^2:=1 and assign(x^2+y^2+z^2+w^2,1) but it doesn't work.

What I should type to make it work?

Thank you

 Obtain the tri-stimulus XYZ values from the CIE Color matching functions.

 Show the gamut of maximum chroma for the standard observer model with a D65 Illuminant.

 Approximate the white point of a Planckian source and compare to D65.

 Translate the maximum chroma gamut in xy to Lab (CIE L*a*b*) for perceived gamut (Violet and Magenta come together)

 Map the RGB color cube of fully saturated color into Lab and compare to perceivable colors.

10/6/15  Initial Document

•12/28/15 Improve RGB gamut with more data points: Procedures added for RGB to Lab: Wavlength Colors now based on CIEDE2000 model for Lab.                   

 Here is the latest version of this document, the MSL_data must be in a directory set in the mw file;

MSL_data.xlsx    Vision_RGB_Gamut.mw