@acer  

Thanks

Could nothing find in old study Maple worksheet about double integrals, the area definitions for domain..

But i see also R={(x,y) |  .....} as a set notation for a domain to use in double integrals. 
The rectangle seems to me correct

[ -4,2]x[-4,5] notation example has special handling if you translate to the x-axis and y -axis in 2D and in 3D to  xyz axises and also in Maple syntax too
But this grid area is wherein the implicit curve must be plotted.   

@acer This is an attempt at part ii) using your earlier methodology of Arrays and loops. You may be able to bend it to your task. You certainly don't have to do it this way. (It's not my preference.)

I don't have another choice to do it on a different way and get now a little bit used to see calculations with arrays.

  

@acer 

That grid thing notation rectangle [-4,2] x [-4,5]  can't give meaning to this
The curve must be plotted in this rectangle ? 

Its clear, but 20 years back fsolve was maybe the only solver in Maple ( old shool )
There are some more as you showed in earlier post
I collected them. 
Add this post at the excersises set task post

@acer 

Thanks!

I was doing exc set2 task 7 (i) (ii),(iii)

The first question for 7(i) ..was about to show a portion of the Curve ? 
Do i understand it well that you did 7(ii) and 7 (iii) ?

@Carl Love 

Thanks

A special case if  dividing/multiplying  by zero is not possible. 
I must see this situation

@Carl Love 

Thank

Don't see yet what decision has to be made in the procedure
Has to with the length of the tangentline?

@acer 

Thanks

Looks good for n = 3 and i did  for n = 10 it is becoming rather small the tangentlines, but if the function is periodic then that portion of the plot counts
But perhaps with zooming in the plot i shall better see the tangentlines?
The whole plot for n = 10 shows mainly the blue points without tangentlines -> zoom in 

Its about the variable L what gives room for experimenting
Note: must study closer how this done the deravation for a variable tangentline length
I noticed horizontal tangentline is max length and minimal when the tangent line is almost vertical
Its a visual confirmation about the steepness of the tangentline

This is better than all tangentlines do have a fixed length  ( no comparison needed with another procedure what has fixed lenghts)

Do see a new programing construct : a if with quotes.

@acer 

Thanks

There was no requirement for how long the tangentlines or  inflectionlines should be in the tasks as i can see it now.
Interesting your solution for the tangent length by not taken a fixed length what i proposed.  

I am curious how this will be look in a general procedure for a any number n of tangentlines
Maybe interesting to compare both procedures for their "tangentlengths looks"?      

@acer 

Thanks

There was the idea of make the procedure general voor een given number n of tangentlines, is it not enough to base the tangentlinelength  on a sub-interval length ( some smaller), that should be enough for all tangentline lengths.
Is that not a easier solution ?

@acer 

Thanks

Suppose the slope is 0 of the tangentline then the length must fit, between a sub interval from interval a b -> the tangentpoint lie on the interval point
Maybe can this length be used for all other slopes of the tangentlines 

l@Carl Love 
Thanks
The length of the tangentlines are +- (b-a)/2n  for a given interval 
This can be a plotoption then.

n is number of tangentlines to make it general, but the task was for 6 tangentlines : a interval a b divided in 5 subintervals.

I will try to make it general the procedure for any number of tangentlines
 

@janhardo 

Tried to make as procedure Tangentlines( f,a,b) input : two number a , b as interval, but failed.
Note : in Holland we are used to one Capital letter for words : example: Raaklijnen is (TangentLines)
 

I succeeded in adding the x-valus for the tangentpoints and adding a legenda in the procedure.

betounes_ex_set_2_opg_6via_codeexample2.3_uitwerking_ac.mw

@Carl Love 

Thanks

Good to point this out and keep in mind 

@acer 

Thanks

Indeed a interesting question: what using a expression or function in a procedure definition?
But reading your post its rather complicated to judge when to use a expression or when a real function

My initial idea was to start with the procedure definition using a and b , startpoint and endpoint of the interval 

proc( f, a::numeric,b::numeric ) ,but then i noticed the range example.
Its only a,b or a..b for procedure input ,without telling what are they standing for in the procedure for a new user. 

@Carl Love 

Thanks!

I will try do my best more on my English and beware to ask a open question , because its confusing.
It was not that i ask for sure to you, to give a partial sum procedure, but got one, thanks for that.

Outcomment is text or code with # or with  /*   */ , the idea that the code is bypassed then.

Note: i tried /*  */ in a do loop contained in a procedure, but that is not working. 
Concerning the summed up issues : all points need more study from my side 

But seeing in example makes more clear.
This code example ,must be reworked

PR:=proc(A,N)   # PR is product
   p:=1;
   for i from 1 to N do p:=p*A[i] end do:
end proc;  

@acer 

Thanks

I study all the attachments.

I am aware of the expression or operator input for a procedure that they differ, how could it go wrong?