My procedure Fsimp uses y(t) only with prime notation, so maybe i can make more general later on, with a fix for de odetest
I like the most @nm 9421 , because the assumption is applied to see on g 

 

Added method:  Odesolve for finding functions with odetest, method= laplace, series and ics 
Odesolve method will be skipped for leafcount and length calculaton ( via a list of exceptions for  skipped methods)
Using prime notation 
Added method: ODEplotseries , makes a direction field with approximation curve (series) ( polynome)
Odetest must be working 100 % ?

FSimp-integration-assuming_Mprimes_17-8-2024DEF_.mw

@MaPal93 
I ask maple coding expert ...

@nm 
"Why is simplify needed to evaluate limit? Is this documented somewhere?"

Because if x = 0 , b remains and a simplify command with assuming option is also possible.
It may be that the simplify algorithm first simplifies the limit question to b? 

"I do not expect that Maple covers everything in teaching"
Well, given the effort Maplesoft is doing for education, so i thought i show my practical examples and wondering.
Jan Douma B Ed math

Maple uses the  form  [ infinity/- infinity]  for  L'Hopital to use  as derived  in another picture , but what is the educational value of this L'Hopital rule ?

Same limit , but  now form [ infinity/- infinity], and Maple goes not further to try to get the value of the limit
This is another form  [ infinity,- infinity]  for  L'Hopital to use 
  

Maple is using SimplifySteps (number 8 in FSimp procedure) here and shows that numerator and denominater are 0 
So, its [0/0]  
But nothing happens further and it should be interesting if L'Hopital is applied and a new limit is calculated 
Limit(-2*x^2*ln(x)^2, x = 0, right), but this is the same situation as for the startlimit 
Another trick is needed.
Perhaps with RuleSteps i get a new( but useless) limit  for the [0,0] ?
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Concerns me if Maple wants to be educational and show in steps of a solution , then also all the steps can be seen in a solution
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In my FSimp procedure i did SimplifySteps on a limit and in my textbook example l'hopital
Seems to be not clear what l'hopital version is used by Maple ( there are two versions [0/0],[infinity/infinity] )


voorbeeld_Mprimesforum_limiet_lhopital.mw

@vv 
Thanks, In the most right limit you can recognize some standardlimits 
But how do you know when to use l'hopital ?

With this little investigation ...
But x.ln x for x->0  gives [ 0, infinity ]  = lim x<- 0  x/ 1/ln x = [0/0] (=l'hopital)

lim x<- 0  1/ (- 1/ ln^2.x). 1/x (l'hopital applied, but it seems to go to limit x<--0  gives   x ln x^2 
Its not going better now with this limit

So we need to rewrite  x.ln x again on a second way...

Tried to add limit rules, but don't know how to handle the Calculus1 infolevel 1 and assigning exactly Calculus 1 package with the Uses cmmand  

FSimp-integration-assuming_Mprimes_26-7-2024.mw

Can now handle a sequence of assumptions

FSimp-integration-assuming_Mprimes_21-7-2024.mw

I solved it for integration : undefined or defined integrals are recognised in FSimp procedure 
A integral with  a assumption  can also be used too

"Now, do you understand that the expression
   u::nonnegint
is not itself an integer? Do you understand that the expression u::nonnegint is not itself of type nonnegint?"
yes, if it not is working

FSimp-integration-assuming_Mprimes_20-7-2024.mw

Simplify with assuming is working, but not working is Definite integral with assumption method yet.
( using the definite integral method instead  of it)
Funny enough method 14 seems to be working with a assumption, while it has no definition for it 
The variable of u in the integral is defined in FSimp procedure
Chanced also the FSimp input names for easier handling and  a assumption message 

FSimp-integration-assuming_Mprimes_19-7-2024.mw

@acer 

Seems not be solving this assuming problem by  using assumption as keyword  : example : assumption=(0 <= u) on 6 th position

e3 := Int(exp(-u*x)*x^(1/3), x = 0 .. infinity);
assumption:= (0 <= u);

FSimp(e3, 15,true,2,false, assumption); # zie het Maple-voorbeeld in de help

FSimp(Int(exp(-u*x)*x^(1/3), x = 0 .. infinity), 15, true, 2, false, 0 <= u)