## How to calculate a definite integral by the method...

Above in the figure, the trapezoid method. How to fix the error?

And how to solve this interval using the method of rectangles?

## i'm realy confused, can anyone help me please ?...

 > sin(Pi/12);
 (1)
 >

can anyone explain to me this result ?

in the book "maple by example" they said that sin(Pi/12);
sin (1/12 π)
returns sin(π/12) because it does not know a formula for the explicit value of sin(π/12). but when i'm calculated this in maple i had got , this result, what does this result mean ?

## why it give me this ?...

we know that the exponotial function is represented as a taylor series, that means that the exponontial of any value is approximatvly evaluated ,the same thing of sinus function when i calcute sin(Pi/6) it give me the exacte result,

 > sum(0^i/i!,i=0..infinity);
 (1)
 > exp(0);
 (2)
 > sin(0.2);
 (3)
 > sin(Pi/6);
 (4)
 > sin(Pi/2);
 (5)
 >

,can anyone explain to me these results ?

## how can i get this ?...

we know that  maple evaluate an expression as a tree, for example if i have the expression:

f:=x^2*exp(3/2)*sin(Pi/3-1/x);

i want to get all the tree, is there a command to obtain this !!

## what is the diffrence between these command...

can anyone tell me the difference between subs and eval and  evalf ?

## How to solve these two problems?...

Hello dear Maple,

My name is Bulat, I'm student of Kazan National Research Technical University ( Russia). In our High Program we used your product ( Maple V, Release 4). Now I have two problems and I haven't no idea how I resolve their. I am forced to ask for your help. I upload PrintScreen of my two problems. Please help me to solve them. I' ll be grateful for your help. Sorry for my English :(.

Yours very truly, Bulat

## Error, too many levels of recursion...

In Maple V, Release 4 (1996):

 T:=table():i:=1:N:=5000;for i from i to N  do   T[i]:=T[i+1]:   T[i+1]:=1;   eval(T[1]);od:print(i);for i from i to N  do   T[i]:=T[i+1]:   T[i+1]:=1;   eval(T[1]);od:print(i);

N := 5000
Error, too many levels of recursion
3607
5001

Can You explain this occurence, as well as the following one:

In Maple V, Release 4 (1996):

 T:=table():i:=1:N:=5000;for i from i to N  do  T[i]:=T[i+1]:  eval(T[1]);od:print(i); for i from i to N  do  T[i]:=T[i+1]:  eval(T[1]);od:print(i);;

gives:

N := 5000
Error, too many levels of recursion
3607
Error, too many levels of recursion
3607

How does one control allowance for recursion depth?

## What is the expected correct outcome of the follow...

In Maple V, Release 4 (1996):

 _EnvX:=0; b:=0; proc() global b; print(_EnvX, b); assign('_EnvX=1, b=1'); print(_EnvX, b); end();_EnvX:=0: b:=0: proc() global b; print(_EnvX, b); _EnvX:=1; b:=1; print(_EnvX, b); end();;

gives:
0, 0
0, 1

 _EnvX:=0; b:=0; proc() global b; print(_EnvX, b); assign('_EnvX=1, b=1'); print(_EnvX, b); end proc();_EnvX:=0: b:=0: proc() global b; print(_EnvX, b); _EnvX:=1; b:=1; print(_EnvX, b); end proc();

?

## Is this a map execute error?...

Code & result:

> map((a::uneval,b)->'args',[a,b,c,d],1..4,x);
['a, 1 .. 4, x', 'b, 1 .. 4, x', 'c, 1 .. 4, x', 'd, 1 .. 4, x']

> map((a,b::uneval)->'args',[a,b,c,d],1..4,x);
[a, 1 .. 4, x, b, 1 .. 4, x, c, 1 .. 4, x, d, 1 .. 4, x]

Why is the output not:
['a', 1 .. 4, x, 'b', 1 .. 4, x, 'c', 1 .. 4, x, 'd', 1 .. 4, x]
and
[a, '1 .. 4', x, b, '1 .. 4', x, c, '1 .. 4', x, d, '1 .. 4', x]
?

## Procedure for Aitkin's Method...

How do I write a procedure to find a root of f(x)=0 in the vicinity of a given value x0. The procedure should initially use the rearrangement method to produce a linearly convergent sequence of values, and should, when appropriate, switch to Aitkin's Method. The input for the procedure should be the re-arranged function and the velue for x0. The output should be the root and the number of iteration taken. The procedure should check that re-arrangement will converge. This program should do in Maple V Release5.

## Obtaining the splitting field...

I am trying to obtain the splitting field of New_polyq. evala@AFactor did not complete. Applying splitting sequentially produced independent extensions from the first 2 (3?) factors. evala@Indep did not complete for the union of all 4 extensions.

What libraries would handle this better?

restart; _EnvExplicit:=false;interface(labelwidth=200);
Rho_polys:=rho[3,1]^3-2, rho[3,2]^2+rho[3,2]*rho[3,1]+rho[3,1]^2, 2*rho[6,1]^3+rho[6,1]^6-2, rho[12,1]^2+rho[6,1]^2-1, 2*rho[12,2]^2-rho[6,1]^2*rho[3,2]*rho[3,1]^2-2*rho[6,1]^2-2;
New_poly:=1/16*(-rho[6,1]^4*rho[3,2]*rho[3,1]-2-rho[3,1]^2*rho[6,1]^4-2*rho[6,1]*rho[3,2]*rho[3,1]-2*rho[3,1]^2*rho[6,1]+2*lambda^2)*(rho[6,1]^4*rho[3,2]*rho[3,1]+2*rho[6,1]*rho[3,2]*rho[3,1]-2+2*lambda^2)*(-2+2*rho[3,1]^2*rho[6,1]+rho[3,1]^2*rho[6,1]^4+2*lambda^2)*(-2+rho[6,1]^2*rho[3,2]*rho[3,1]^2+2*lambda^2);
sol:=solve({Rho_polys});
alias(op(sol));
New_polyq:=subs(sol,New_poly);

Hi, I have a homework to do that I am strugling with:

write a procedure which uses euler's method to solve a given initial value problem.
the imput should be the differential equation and the initial value.
using this programme find y(1) if dy/dx= x^2*y^3 and y(0)=1, and use maple dsolve command to check the solution.

That is what I have managed to do, but somehow it is not working correctelly, can somebody help please?

eul:=proc(f,h,x0,y0,xn)
local no_points,x_old,x_new,y_old,y_new,i:
no_points:=round(evalf((xn-x0)/h)):
x_old:=x0:
y_old:=y0:

for i from 1 to no_points do
x_new:=x_old+h:
y_new:=y_old+evalf(h*f(x_old,y_old)):
x_old:=x_new:
y_old:=y_new:
od:
y_new:
end:

Thanks

## taking limit with assume on indexed variable on li...

```I am also having trouble with limits when I have indexed
variables.   That is, how do I tell Maple to assume every element of
an indexed variable is positive?

uxb3% maple < te7a

|\^/|     Maple V Release 3 (Governors State University)

Here, I show that normal limits work.
> int (exp(-x^2),x=3..infinity);

1/2         1/2

1/2 Pi    - 1/2 Pi    erf(3)

> assume(a>0);

> int(exp(-a*x^2...```

## How would I write the procedure?...

`I use the eqn feature from Maple to generate troff output.Each equation is longer than one line.  How does one get the eqn/troffcombination to automatically break the equation into multiple lines.(I tried finding the division point myself and could not do it.  I am generating the output and I have a perl script that puts together the indivdualequations into the document to be printed.  Thus, I need something automatic)I tried Google and...`