> with(Student[Calculus1])

>TangentTutor(1/(3*x+1))

choose x=2, #of increment 4, click on plot options and choose x=0..6,y=0..1, then click on animate. Then you click on close and the animation will be in your worksheet.  You click on the plot an you will see the playing button in the toolbar.  Chose the "next frame" and click one by one and you should understand the difference between secant and tangent and you just have to understand the link between this and (f(x+h)-f(x))/h

> with(Student[VectorCalculus]);
> with(Student[Precalculus]);
> with(plots);
> A := [1, 2]; B := [3, 6]; C := [8, 4];
> ABm := Midpoint(A, B);
> ACm := Midpoint(A, C);
> BCm := Midpoint(B, C);
> p1 := plot([A, B, C, A], x = 0 .. 10, y = 0 .. 10);
> p2 := plot([A, BCm], x = 0 .. 10, y = 0 .. 10);
> p3 := plot([B, ACm], x = 0 .. 10, y = 0 .. 10);
> p4 := plot([C, ABm], x = 0 .. 10, y = 0 .. 10);
> p5 := textplot([op(A), "A"], align = {above, left});
> p6 := textplot([op(B), "B"], align = {above, right});
> p7 := textplot([op(C), "C"], align = {above, right});
> p8 := textplot([op(ABm), "ABm"], align = {above, left});
> p9 := textplot([op(ACm), "ACm"], align = {below, right});
> p10 := textplot([op(BCm), "BCm"], align = {above, right});
> p11 := textplot([4, 4, "P"], align = {above, right});
> plots:-display(p || (1 .. 11));

Now, you have to define the steps that will give you P.  Do some work in a Maple worksheet and uploadit in mapleprimes (using the up green arrow).  Starting from there, we will see in wich way we can help you without giving you the complete solution.

 The ebook install by default at:

c:\Program Files\Maple 12\toolbox

And there is the file Table of Contents.mwz

For my part, I simply create a shortcut.  Of corse, it would be fantastic if you could have a "toolBox" menu in Maple and each time you install a ebook, it will be available in that menu.

BTW, very interesting what you show about the context-menu Acer.

> PS := proc ()

local E;

 E := readstat("Enter the value of E :");

 if E < 10 then E:=E^2 else E:=0; end if;

 printf("V=%d\n", E);

 end proc;
> PS();

 Here is how to expor to a file

> with(LinearAlgebra);
> for i to 3 do
 v[i] := <(x[i], y[i])>;
 vt[i] := Transpose(v[i]);
end do:

> M := <vt[1], vt[2], vt[3]>

                                      [2  3]
                                      [    ]
                                 M := [3  4]
                                      [    ]
                                      [2  0]

> ExportMatrix("D:/Data/Data6/My_Filea.txt", M, format = rectangular);
> fclose("D:/Data/Data6/My_Filea.txt");
> restart;
> M := ImportMatrix("D:/Data/Data6/My_Filea.txt", format = rectangular);

                                      [2  3]
                                      [    ]
                                 M := [3  4]
                                      [    ]
                                      [2  0]

Hope it help.

for your patience.

 Thanks Axel,

Up until

 limit(%,k=infinity);
                                  1

is very simple (Hospital's rule twice).  Where I am stuck is only this:

> R := k-> (4*k^2-6*k+(-p-2)*(p-1))/(4*k^2-2*k) ;

                                2                         
                             4 k  - 6 k + (-p - 2) (p - 1)
                   R := k -> -----------------------------
                                         2                
                                      4 k  - 2 k          
> R1 := series(R(k), k = infinity, 2)*x^2;

                                /    1    /1 \\  2
                          R1 := |1 - - + O|--|| x 
                                |    k    | 2||   
                                \         \k //   

it's quite obvious that |x|<1 and k=1,2,3,4... for the convergence.
I see that the denominator will always be positive in R and so

                           2                        
                        4 k  - 6 k < (p + 2) (p - 1)

But how Maple deal with k = infinity to obtain R1????  This is taken from a book

(where n is p for us)

So I am not dreaming but surely stuck on how Maple get R1.

Please try one more time.  After that, I quit..........

 With it, I solve it exactly and understand it and find the link between LegendreP and LegendreQ from 2F1.

But still I don't understand how Maple give the following:

> n1 := expand(-(p-2*k+4)*(2*k-3+p));

                              2          2            
                      n1 := -p  - p + 4 k  - 14 k + 12
> d1 := expand((2*k-3)*(2*k-2));

                                     2           
                            d1 := 4 k  - 10 k + 6
> R := series(n1/d1, k = infinity, 2)*x^2;

                                /    1    /1 \\  2
                           R := |1 - - + O|--|| x 
                                |    k    | 2||   
                                \         \k //   

I need to know how to do it by hand on a blackboard.  The reasonning behind this result.  Is there something I don't get?

That I know.  In fact i would like to know how I would obtain

                                      1    /1 \
                             R := 1 - - + O|--|
                                      k    | 2|
                                           \k /

in front of a blackboard without Maple.

And I still wondering about passing from Hypergeom to Legendre as you can see int the attach file Legendre.mw

Thanks in advance for the trouble.

  How do Maple calculate the ratio R when k=infinity ????????

I would like to do it by hand firts before relaying on Maple.

I found this on the web

                                                            2
                |  a(k)  |     (p - 2 k + 4) (p + 2 k - 3) x 
                |--------| = - ------------------------------
                |a(k - 1)|          (2 k - 3) (2 k - 2)      

> n1 := expand(-(p-2*k+4)*(p+2*k-3));

                              2          2            
                      n1 := -p  - p + 4 k  - 14 k + 12
> d1 := expand((2*k-3)*(2*k-2));

                                     2           
                            d1 := 4 k  - 10 k + 6
> R := series(n1/d1, k = infinity, 2);

                                      1    /1 \
                             R := 1 - - + O|--|
                                      k    | 2|
                                           \k /

So my series converge at least conditionnally if -1<x<1 .   How do Maple calculate the series when k=infinity ????????

> L := [[1, 4.9], [2, 4.8], [3, 5.1], [4, 5.0], [5, 5.5], [6, 5.5], [7, 5.7], [8, 6.1], [9, 6.1]];

L := [[1, 4.9], [2, 4.8], [3, 5.1], [4, 5.0], [5, 5.5], [6, 5.5], [7, 5.7],

  [8, 6.1], [9, 6.1]]
 

> with(CurveFitting);
> Interactive(L, x);
                        4.544444444 + 0.1733333333 x
 

In the interactive box, you will see Enter an expression in x [ a*x+b)], then click plot.  You will see the regression line.  When you click on Done, you will have the equation of the regression line.

CurveFitting is the place to!

 I was thinking series while in fact I was working on sequence.  Time to go to bed.  Sorry for douting of csum..