## Convert expression to LaTeX...

How to convert expression below to LaTex:  $\lim _{x \rightarrow 2} \frac{2}{x+3}$

And How to convert expression below to LaTex:  $\int_{2}^{3} \frac{1}{x^{2}+2} d x$

file test: newLaTex.mw

## Incorrect definite integration of hyperbolic funct...

Hi Guys,

I am trying to intgrate a function involving hyperbolic functions in a range of 0 to 1 and it is giving me very large value of 10^94. However, on doing integration terms terms i can see that some large terms involving 10^191 cancel out with each other and I can have a fnite value of this integration. It would be really helpful if someone can help me out why it is happening with int function and how can I solve this case involving hyperbolic function. For reference maple file is attached. Thanks in advance and much appreciated.

With Regards

Sunit

question.mw

## How to simplify multiple definite integrals...

Hi Guys,

I need help regarding simplifying definite integrals. I have following expression

As we can notice the limit for each integral is same, so I should be able to take these integral limit outside. I am trying to use collect and simplify, but both of these command are not working. It would be really helpful for me if I can get the solution for it.

Please find the attached example sheet also.example.mw

With Regards

Sunit

## How to use factor elementwise?...

Hi Guys,

It might be a very basic question, but I am struggling with it for a quite a time.  I have an expression in a form of

f(x)=h(x)+g(x);

and I want to use factor operation elementwise, i.e., it can individually act on h(x) and can give me

f(x)=h1(x)*h2(x)+g1(x)*g2(x). But whenever I am putting factor operation with elementwise it is not giving me desired answer. It would be really helpful and great if someone can help me out.

I am attaching maple sheet for reference also.

## Solving a Quadratic Diophantine Equation with 3 va...

How do I find integer solutions to this non-linear equation:

8= 7(x^2+y^2+z^2)+2x+4y-8z.

Tried isolve and it wasn't working. (I guess too many variables?)

Also, if f(x,y,z) is the RHS, how do I write a loop that finds integer solutions to f(x,y,z)=c for |x|,|y|,|z|< N, say?

## error: fsolve unrecognized form...

Hello,

I don't understand why Maple gives me the following error:

Error, (in fsolve/Iterators) unrecognized form

The full maple file:

 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 (1)
 >
 (2)
 >
 (3)
 >
 (4)
 >
 (5)
 >
 (6)
 >
 (7)
 >
 (8)
 >
 (9)
 >
 (10)
 >
 (11)
 >
 (12)
 >
 (13)
 >
 (14)
 >
 (15)
 >
 (16)
 >
 (17)
 >
 (18)
 >
 (19)
 >
 >
 >

Thank you!

## How to display each vector turn on the same axis o...

How do I draw three vectors on the same axis of coordinates, I see this vector appear after the previous vector one second  and on the screen when this vector appears, the previous vector remains on the screen and on the last screen I see all three vectors with the Maple command?

Example : plottools :- arrow( [1, -2], [4, -1], 0.001, 0.05, 0.1), plottools :- arrow( [-1, 3], [2, 1], 0.001, 0.05, 0.1), plottools :- arrow( [0, 2], [-3, 0], 0.001, 0.05, 0.1).

Thanks so much for the help of everyone!

## How to display each chart turn on the same axis of...

How do I draw three graphs on the same axis of coordinates and I see this graph appear after the previous graph one second with the Maple command? Example : y = x, y = x2, y = 1 - x.

Thanks so much for the help of everyone!

## How to use the add command in this scenario...

Lecture 4 - Problem 2
a)
> a := -2100; b := 2100; N := 8; h := (b-a)/N; C := 4491; x := [seq(h, h = -2100 .. 2100, h)]; y := proc (x) options operator, arrow; sqrt(1+((1/2)*exp(x/C)-(1/2)*exp(-x/C))^2) end proc; evalf(y(x[1])); evalf(y(x[N+1])); L := (1/3)*h*(y(x[1])+4*(y(x[2])+y(x[4])+y(x[6])+y(x[N]))+2*(y(x[3])+y(x[5])+y(x[N-1]))+y(x[N+1])); evalf(L);
-2100
2100
8
525
4491
[-2100, -1575, -1050, -525, 0, 525, 1050, 1575, 2100]
/                           2\
|    /1    /x\   1    /  x\\ |
x -> sqrt|1 + |- exp|-| - - exp|- -|| |
\    \2    \C/   2    \  C// /
1.111332350
1.111332350
(1/2)
/                               2\
|    /1    /-700\   1    /700 \\ |
175 |1 + |- exp|----| - - exp|----|| |
\    \2    \1497/   2    \1497// /

(1/2)
/                              2\
|    /1    /-175\   1    /175\\ |
+ 700 |1 + |- exp|----| - - exp|---|| |
\    \2    \499 /   2    \499// /

(1/2)
/                               2\
|    /1    /-175\   1    /175 \\ |
+ 700 |1 + |- exp|----| - - exp|----|| |
\    \2    \1497/   2    \1497// /

(1/2)
/                               2\
|    /1    /175 \   1    /-175\\ |
+ 700 |1 + |- exp|----| - - exp|----|| |
\    \2    \1497/   2    \1497// /

(1/2)
/                              2\
|    /1    /175\   1    /-175\\ |
+ 700 |1 + |- exp|---| - - exp|----|| |
\    \2    \499/   2    \499 // /

(1/2)
/                               2\
|    /1    /-350\   1    /350 \\ |
+ 350 |1 + |- exp|----| - - exp|----|| |      + 350
\    \2    \1497/   2    \1497// /

(1/2)
/                               2\
|    /1    /350 \   1    /-350\\ |
+ 350 |1 + |- exp|----| - - exp|----|| |
\    \2    \1497/   2    \1497// /

(1/2)
/                               2\
|    /1    /700 \   1    /-700\\ |
+ 175 |1 + |- exp|----| - - exp|----|| |
\    \2    \1497/   2    \1497// /
4354.742601
> L := (1/3)*h*(y(x[1])+4*add(y(i), i = y(x[2]) .. y(x[N]), 2)+2*add(y(i), i = y(x[3]) .. y(x[N-1]), 2)+y(x[N+1])); evalf(L);
4354.742601

## How do i get my computation time...

I am trying to compare time taken in minutes for each iterative model(Jacobi, Gauss-Seidel and SOR) to complete, so as to figure out the iterativre model with a faster time of convergence but i don't know the command to initiate.

## how to find equation of intersection between a pla...

Hi
i need to find equation of intersection between a plane(Z=0)  and 3d curve like below:

plane :  Z=0

curve:

sqrt(G*(2-G))+(1-G)*(arccos(G-1)+(1/5)*Pi)+k*sqrt(G*(2-G))*cos(sqrt((1+k)/k)*arccos(G-1)+(1/5)*Pi)+sqrt(k/(1+k))*(1-G)*k*sin(sqrt((1+k)/k)*arccos(G-1)+(1/5)*Pi)

I ploted Z=0 plane and that curve . it is like this .
i want equation of the pointed curve(curve equation of intersection between Z=  and curve )in bellow  such as k=f(G) .

best regards

## maple dosent solve my problem?...

i have a assignment problem to optimize with 1200 variables and almost 1000 constraints. but maple couldnt solve it. anyone who can help me is welcome

or may i try another app?

thanks

this is the my model
tam2.mw

 > restart;
 >
 >
 > we:=[1,2,8,9,15,16,22,23,29,30];
 (1)
 > wd:=[3,4,5,6,7,10,11,12,13,14,17,18,19,20,21,24,25,26,27,28];
 (2)
 > #printlevel :=3;
 > for j from 1 to 30 do #her gündüz vardiyasında en az 4 hemşire bulunsun a[j]:=sum(x[i][j][1], i=1..20)>=4: end do;
 (3)
 > A := [seq(a[j],j=1..30)];
 (4)
 > #her gece vardiyasında en az 4 hemşire bulunsun for j from 1 to 30 do b[j]:=sum(x[i][j][2], i=1..20)>=4: end do;
 (5)
 >
 > B := [seq(b[j],j=1..30)];
 (6)
 > #her hemşire ayda en az 4 hafta içi gündüz vardiyasında çalışsın for i from 1 to 20 do c[i]:=sum(x[i][wd[k]][1], k=1..20)>=4: end do;
 (7)
 > C := [seq(c[i],i=1..20)];
 (8)
 > #her hemşire ayda en az 4 hafta içi gece vardiyasında çalışsın for i from 1 to 20 do d[i]:=sum(x[i][wd[k]][2], k=1..20)>=4: end do;
 (9)
 > dd:= [seq(d[i],i=1..20)];
 (10)
 > #her hemşire ayda en az 2 hafta sonu gündüz vardiyasında çalışsın for i from 1 to 20 do e[i]:=sum(x[i][we[k]][1], k=1..10)>=2; end do;
 (11)
 > E:= [seq(e[i],i=1..20)];
 (12)
 > #her hemşire ayda en az 2 hafta sonu gece vardiyasında çalışsın for i from 1 to 20 do f[i]:=sum(x[i][we[k]][2], k=1..10)>=2; end do;
 (13)
 > F:= [seq(f[i],i=1..20)];
 (14)
 > #gece vardiyasında çalışan hemşire ertesi gündüz ve gece vardiyalarında izinlidir for i from 1 to 20 do for j from 1 to 29 do g[i][j]:=2*x[i][j][2]+x[i][j+1][1]+x[i][j+1][2]<=2 end do; end do;
 > for i from 1 to 20 do g[i] := seq(g[i][j],j=1..29) end do;
 > g:= [seq(g[i],i=1..20)];
 > with(Optimization);
 > Minimize( sum(t[m], m=1..20),{A[],B[],C[],dd[],E[],F[],g[]}, assume = binary );

## Ordinary differential equations...

Hi guys,

This is the first time of solving partial differential equation, can some please help me point out some errows in my code.

 >
 >
 (1)
 >
 (2)
 >
 (3)
 >
 (4)
 >

Fig. 3 (changing values of Ha):

 > P:= Ha: vals:= [1, 5, 10, 20]: sols:= [seq(Solve(P= v), v= vals)]: colors:= [red, green, blue]: for F in [v,theta,phi](y) do    print(plots:-display(       [seq(          plots:-odeplot(sols[k], [y,F], color= colors[k], legend= [P= vals[k]]),          k= 1..nops(vals)       )],       labeldirections= [horizontal,vertical]    )) od:
 >

## problem solve a system in maple...

i have a problem to solve this system ?

## How to transform a function plot by "shifting" hor...

Hello,

I will explain my problem on a simple function and some data.

mg:=78.54*7.85*1e-9*1000*9.81;l:=10000;l0:=12000;h:=0;H := 28.399;
eta:=mg*l/(2*H);
zeta:=arcsinh(mg*h/(2*H*sinh(eta)))-eta;
z:=H/mg*(cosh(mg/H*x+zeta)-cosh(zeta));
plot(z,x=0..l);

Above is a definition of an initial plot. Now I would like to draw a new plot in which every x coordinate is shifted horizontally by a function:

deltax:=H*arcsinh(x)-x;

As you see I can't use translate or scale so I've tried to use a transform function but I can't do it the right way.

I would be grateful for any ideas.

Greetings,

Iza

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