## computing the limit of the function sequence...

My post is not actually a question but a complaint. I'm trying to prepare a worksheet for teaching function sequences with Maple but Maple always make me sad. ``` > assume(x::RealRange(-1/2,1/2), n::integer): > limit(x^n, n=infinity) ``` Limit(x^n, n=infinity) but ``` > assume(x::RealRange(-1/2,0), n::integer): > limit(x^n, n=infinity) ``` 0 ``` > assume(x::RealRange(0, 1/2), n::integer): > limit(x^n, n=infinity) ``` 0 I'm running Maple V9.5. Is it getting better in later versions?

## How do you display multiple coordinate frames, in ...

I would like to display in one output, multiple coordinate systems. For example, I have a regular coordinate system, and another one that is rotated. I would like to display both of these coordinate systems, that is one coord. overlayed on the other, in the one output. Can any one help me?

## Perfect Numbers...

Does Maple have any information on perfect numbers ? Also, if it does have some information, how many perfect numbers is Maple knowledgeable of ? v/r,

## ln in symbolic mode...

Hi. I'm having a problem getting questions involving ln()and abs() operators to evaluate correctly. For example, when creating maple graded questions, I set the correct answer to say ln( abs( x^3 + 12 ) ). So when the student enters this answer in text mode, everything is fine. In symbolic mode if ln( |x^3 + 12| ) is entered everything is fine, however, if ln|x^3 + 12| is entered, maple TA says wrong. The lack of parenthesis gives a wrong answer. Does anyone know how to make maple TA more tolerable in this situation to evaluate ln|x^3 + 12| as a correct answer? Thanks

## new at maple.what does _Z means?...

I'm completely new at maple. I'm solving this equation:

eqn := exp(-a*x)*exp(-b*x)-exp(-c*x)*exp(-d*x)=exp(-a*x)-exp(-c*x);

solve( eqn, {x} );

This is what I get:

eqn := exp(-a*x)*exp(-b*x)-exp(-c*x)*exp(-x*d) = exp(-a*x)-exp(-c*x) {x = -RootOf(exp(_Z+c*_Z/d)-exp(_Z*(a+b)/d)+exp(a*_Z/d)-exp(c*_Z/d))/d}

I can't find what _Z means .Can anybody help? Thanks in advance

## Try this...

>restart: >_EnvAllSolutions:=true; >solve(sin^2(x)/x=0); Pi(2_Z1~+_B1~),Pi(2_Z1~+_B1~) >fsolve(sin^2(x)/x=0); -3,141592654 That means that Pi(2_Z1~+_B1~),Pi(2_Z1~+_B1~)is equivalent to just -Pi which is not true. What is going on here?

## How do I speed up numerical integration of Bessel ...

I am trying to evaluate the following integral to a float for various values of Zeta and rho. Evaluation of the integral seems to be very slow. Any suggestions on speeding it up? (I am a Maple newbie). "int(exp(-Zeta*eta)*BesselJ(0,rho*eta)*cos(eta),eta = 0 .. infinity)-int(exp(-Zeta*eta)*BesselJ(0,rho*eta)*sin(eta)/eta,eta = 0 .. infinity)+Zeta*int(eta*exp(-Zeta*eta)*BesselJ(0,rho*eta)*cos(eta),eta = 0 .. infinity)-Zeta*int(exp(-Zeta*eta)*BesselJ(0,rho*eta)*sin(eta),eta = 0 .. infinity)" Rgds, Saka.

## Getting Maple to re-arrange equations?...

Is there any command that will get Maple to explicitly re-arrange an equation for another variable? e.g Taking a simple example, y = x + 1 and then getting it re-arranged to x = y - 1

## Dirac function, DTFT and possible numerical integr...

Hi, I'd like to proof: int(sum(2*Pi*Dirac(w+2*Pi*k)*e^(j*w*n), k = -infinity .. infinity), w = -infinity .. infinity) = 1. Can anyone help?

## Fast dialog-less entry of equation labels...

Is there a keyboard-only way to enter equation labels that will not 'zap' the focus away to a dialog box just to enter a label? While the 'look' of the equation labels is kind of nice, I find entering them extremely annoying (zapping focus is really awful UI design).

## Plotting data from arrays...

I was hoping to get some help with a problem I've been facing for the past couple of days. Basically, I've got a quadratic which I've solved for, and found 2 complex roots, say x1 and x2, for a range of values, y. This data has since been put into an array, showing both the real and imaginary parts of the roots. The 2 roots obtained for each value of y are just the positive and negative of each other. I've then taken the data from the array, and since I'm only interested in the imaginary parts of x, I've taken the data from the array and using the seq command, obtained a list of the points x1, x2 and y I want to plot.

## How to plot functions that would be joined on one ...

How to plot functions that would be joined on one diagram? > > > How can these functions Mg_1(x), Mg_2(x), Mg_3(x), be joined in one diagram? These functions are only examples and there can be more of them (as many as the elements of the constructions). > > restart; > element A_B > > Mg_1:=x->(8/25*q*(5*l-x)^2-9/5*q*l*(5*l-x)): > Mg_1(x); > q:=1:l:=10:x1:=5*l: > plot(Mg_1(x),x=0..x1); > element B_C > q:='q':l:='l': > Mg_2:=x->(-3*q*l^2+q*l*(4*l-x)): > Mg_2(x); > q:=1:l:=10:x2:=4*l: > plot(Mg_2(x),x=0..x2); > > element C_D > q:='q':l:='l': > Mg_3:=x->(-q*l*(3*l-x)):

## dsolve(numeric) procedure; returning values other ...

I am using dsolve(numeric)with the procedure option to output the position of a body subject to acceleration. The results(position and velocity) are written into an array for the specified time-points. It all works fine. I use NLPSolve within the procedure called by dsolve as an intermediate step to calcualting the specified acceleration of the body. Is there a way to return the values calculated by NLPSolve? I can back-calculate from the output array values but it is extremely tedious. I can also view the results of NLPSolve using lprint but it is not clear how these results relate to the specified time points and I would want to store the values in a matrix.