## limit of sequence at infinity bugs

by: Maple

The following limit does not return a value. Then the evalf gives a wrong answer.

The answer should be "undefined" or -infinity .. infinity.

limit(exp(n)/(-1)^n, n = infinity) assuming n::posint; evalf(%);

/exp(n)              \
limit|------, n = infinity|
|    n               |
\(-1)                /

0.

The same happens if you delete the assumption.

A similar problem occurs with

limit(sin(Pi/2+2*Pi*n), n = infinity) assuming n::posint;
-1 .. 1
without the assumption this would be appropriate.

## how to evaluate floor...

Why does the following statement not evaluate, or better yet, how can I make it do so?

A:=value(floor(p)) assuming p>0,p<1,p::real;

or

A:=simplify(floor(p)) assuming p>0,p<1,p::real;

or any one of a lot of different attempts along the above lines, all of which seem (to me) that they should yield

A:=0

rather than

A:=floor(p)

which is what I get.

 >
 (1)
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 (2)
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 (3)
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## Looking to collect constant terms from an expressi...

I have a situation

`restart:with(IntegrationTools):with(PDEtools):declare(w(r));assume(delta::constant, R::constant, K:: constant, U::constant):`
`ODE_1:=diff(w(r),r)+R*(diff(w(r), r))^3-K/r;`
` `
`declare(u(r));ODE_T_1:=collect(algsubs(w(r)=u(r)+(r-1)*(U-0)/(delta-1), ODE_1),diff(u(r), r)) ;`
`eq1:=int(phi[i](r)*ODE_T_1,r=1..delta) assuming delta > 1;`
`eq2:=Expand(eq1);`
`eq3 := applyop(u->Parts(u,phi[i...`

## Simplifying expressions(symbolic integration)...

Hi all,

I have the following functions.

`restart:with(IntegrationTools):N:=4:i:='i':for i from 1 to N do    assume(x[i-1]::constant):    assume(x[i+1]::constant):    assume(x[i-1]::constant):    assume(h::constant):`
` phi[i](t):=piecewise(t>=x[i-1] and x[i]>t, (t-x[i])/(h), x[i]`
`(x[i+1]-t)/(h), 0);`
`end do;`
`## my goal is solve the integrals involving phi[i]'s as integrand and x[i]'s as its limits.`

## incorrect improper integral

by: Maple 16

This example was reported to me after a Calculus II student encountered this ridiculous result:

`f := (k+5)/sqrt(k^7+k^2):Int( f, k=1..infinity ):% = value( % );             /infinity                                          |              k + 5                                |          -------------- dk = -infinity            |                   (1/2)                          /1          / 7    2\                                           \k  + k /                    `

## problems with assume...

Dear Maple Users,

I'm solving quite a complicated task, so I tried to simplified an example.

There is an equation:

SOL := fsolve(Nz+int(int(StrssCctXY(x, y), x = -(1/2)*b .. (1/2)*b), y = -(1/2)*h .. (1/2)*h) = 0, {C1 = -(1/2)*h .. (1/2)*h})

StrssCctXY(x,y) is piecewise function containing C1 variable, to solve an equation I had to use assumptions on C1 via assume(C1<num1, C1>-num2) command, after that C1 becomes C1~;

## Problem with assuming...

can you explain me when i solve equation beta-t*beta=0 with condition beta<>0. I write command:
r :=solve(beta-t*beta, t, UseAssumptions), assuming beta <> 0
It works well. But it will be a problem when command is:
r :=solve(beta-t*beta, t, UseAssumptions), assuming beta <> 0, gamma<>0;
Error: Error, (in assuming) when calling 'assume'. Received: 'cannot assume on a constant object'.
thank you very much.

## simplification example...

How can I most succinctly and straightforwardly get Maple to simplify f below to g below?

```> f:=(6*x^2-6*x+6)^(1/2)*(2*x^2-2*x+2)^(1/2);

(1/2)                 (1/2)
/   2          \      /   2          \
\6 x  - 6 x + 6/      \2 x  - 2 x + 2/

> g:=simplify(f) assuming x::real;

(1/2) / 2        \
2 3      \x  - x + 1/

> simplify(g-f...```

## What to do so that maple can integrate the followi...

I need maple to perform the following:

"int((1+m^2*(alpha-theta)^2*sin(theta)^2/sin(alpha)^2/alpha^2)^(1/2),theta = 0 .. alpha)"

but maple does not integrate. I have tried assuming that the term inside the square root is positive, with no result. What else can I do?

## Real trouble integrating this expression? Do you k...

I really need a result to the integration below but Maple 13 just won't return one. Could you please help me or advise me as to what might be wrong or what I might try ? I'm integrating on the real line in x but even when I alter the limits of integration maple just returns the integrand.

s1:= int((1/8)*sqrt(2)*exp((1/2)*k^2*cos(x)^2/sigma^2)*exp(-(1/2)*k^2/sigma^2...

## Understanding the simplify function - different op...

Please help me to make sense of the ways to use the simplify function. In this particular case Maple does some computation and gives me some huge output which I paste below. When I try to simplify the huge output Maple just hangs. But if I use varied commands of simplify detailed below such as simplify(huge_output,symbolic)  or  simplify(huge_output,size)  Maple gives me an output but none of the output are equal to each other and I also noticed that in one instance...

## Does this series converge?...

Why does this happen to Maple 15?

`assuming`([sum(k*p*Beta(k, p+1), k = 1 .. infinity)], [p > 1]); eval(%, p = 2)

Is it possible to show with Maple that for any real p>1 the series converges to p/(p-1), e.g.,

`assuming`([sum(k*p*Beta(k, p+1), k = 1 .. 1000)], [p > 1]): subs(p = 2, %): evalf(%)

How do I show this symbolically? Thanks.

## simplify sin/cos with multiples of Pi...

In the following examples I attempt to remove integer multiples of Pi from sin/cos. Nothing works.

Why? How do I make it work?

Thank you.

term1:=cos(Pi*(3*a-2*n));
> term2:=cos(3*Pi*a+2*Pi*n);
> term3:=cos(3*Pi*a-2*Pi*n);

term1 := cos(Pi (3 a - 2 n))

...