the question is as follow:

The partition does not always have to be equal intervals. Consider evaluating f(x)=x³ between 3 and 5, but splitting up the interval into a partition in which the end points of the subintervals are in a geometric progression. The common ratio r has to be chosen so that 3 is the first term and 5 is the last. Also the subintervals must be capable of getting smaller as n the number of subintervals increases. Check that the geometric series

a, ar, ar², ar³,.....arⁱ, .....arⁿ =b

with r=  and suitable choices for a and b satisfies these criteria. Treating the difference between arⁱ and ar^(i-1) as the width of the subinterval and using the right hand endpoint of the subinterval, evaluate the Riemann sum to n terms for f(x)=x³. Find the limit as n tends to infinity to show that the partition does not affect the result.

here is what i have got so far, can anyone check if im doing it right? thanks

>a:=3:

>b:=a*r^10:

>r:=(5/3)^1/10:

>for i from 0 to 5 do a*r^i end do; -> a list of number appear in sequence ie:3, 3.157...,3.323...3.497...etc

>restart;

>a:=3:

>b:=a*r^100:

>r:=(5/3)^1/100:

>dxj:=a*r^i-a*r^i-1

>xj:=i*dxj+a

>f:=x->x^3

>evalf(sum(f(xj^*)dxj,i=1..100)) -> my value is sth like 162.4788870...

I tried to find the limit, but maple 16 freezed so i think i must have done sth seriously wrong?

<math xmlns='http://www.w3.org/1998/Math/MathML'><mrow><mi>b</mi><mo>&coloneq;</mo><mi>a</mi><mo>&sdot;</mo><msup><mi>r</mi><mrow><mn>10</mn></mrow></msup><mo>&#x3b;</mo><mo>&nbsp;</mo></mrow></math>

Is there any way to write a function that determines the area of any n-sided polygon determined by a sequence of points? ie [[x_1, y_1]. [x_2, y_2], ... [x_n, y_n]] while returning 0 if any of the 2 segments intersect, otherwise print the area. Thanks for any help

Hello,

would you please help me how can i introduce a probability distribution function to maple in document mode?

I want to calculate integral of x f(x)dx, while I want maple to know f(x) is a probability distribution function.

I do not have any assumption about f(x)(for example normal or exponential distriburion)

Thanks

Hello, everyone!

Last week I’ve encountered problems with integration of Maple 17 in Microsoft Office Excel 2013. The Maplesoft note on the point (http://www.maplesoft.com/support/faqs/detail.aspx?sid=32651) offers some ways of fixing it up, though I’ve run all of them the problem is the same:

While the connection is established, after entering the formula “=Maple(“x+x”)”, the Excel returns “Critical Error in Formula”

Before contacting the Maplesoft Technical Support, I want to ask here whether someone had the same case and managed to solve it.

Many thanks in advance.

I have f₁=x, and f_n=x+sin(f_n-1).

I would like to write a procedure that would allow me to find the first derivative of f_n. Thanks.

the question is as follow:

1)receive two integers p and q

2)declare two local p1 and q1 and give them intial values and q

3)check if p o q are equal or less to zero print works only with positive integers

4)while p1 not equal to q1 then p1-a1 otherwise q1-p1

5)whenever p1=q1 we have the GCD

note:must use procedure and call it for different values of p and q after the procedure is written

-by following the instruction above this is what i got

GCD:=proc(p,q)

local p1,q1;

p1:=p;

q1:=q;

if p<=0 OR Q<=0 then 'works only with positive integers'
else while p1<>q1 do if q1<p1 then p1-q1 else q1-p1

end if;

end do;

end if;

end proc;

but when I call two integers eg:p=2, q=6 -> GCD(2,6) maple just freeze...evaluating....forever. is it because i got the procedure wrong etc? it would be helpful if anyone can help me with this. thanks

A square has 36 sub-squares in it. How to Number each sub squares from 1 to 36, to make the sum of vertical, the sum of horizontal, and the sum of cross line are the same .Describe in general if possible.

I am using the ColumnSpace command (from the LinearAlgebra package) to generate a basis for the column space of a matrix. Is there any way to "force" the command to express the basis in terms of columns of A and not in the canonical form with leading 1's?

For example, for

A:=Matrix([[-3,6,-1,1-7],[1,-2,2,3,-1],[2,-4,5,8,-4]]):

I would like to obtain the following basis for the column space:

{[-3,1,2],[-1,2,5]}

I want to plot my function f(x)=sin(e^x +1) and its third order taylor polynomial on the same graph. My code so far (which is giving me an error when I try to define i) is:

f:=x->sin(exp(x)+1);

with(Student[NumericalAnalysis]):

g:=TaylorPolynomial(f(x),x,order=3);

unapply(g,x);

h:=plot(f,0..3,-2..2,color=blue);

i:=plot(g,0..3,-2..2,color=red);

with(plots):

display({h,i},axes=boxed,title=`The function f and its Third Order Taylor Polynomial`);

Thanks.

I have a set of around 60 linear equations with symbolic coefficients. ie

a*x₁ + b*x₂ + ... + c*x₆₀ = 1

x₁ + (c-a)*x₂ + ... + d*x₆₀ = 0

...

c*x₁ + d*x₂ + ... + b*x₆₀ = a

The coefficients a,b,c,d are functions of x₁...x₆₀. I am trying to find the values of these coefficients. When I had a smaller set of equations I was solving them symbolically to find x₁...x₆₀ in terms of a,b,c,d and then using this solution to solve for a,b,c,d. I can no longer solve the set of equations symbolically as it is too large. How do I find the coefficients? I had some sort of optimization routine in mind.

Bonjour

Comment se calcul le résidue d'une fonction f(x,y) ?

Si par exemple f(x,y)=1/x+1/y+5/(x*y), alors le residue de f en (0,0) est défini comme étant (1/2*Pi)^2*int(f(x,y)) avec intégrale est sur une sphère qui contient l'origine.

Est ce qu'il est égal au coefficient 5 de 1/(x*y) dans le developpement de laurent en deux variables ??

Merci d'avance,

Gérard.

Solve the following initial value problem for y(t), z(t).

dy/dt + dz/dt =t

dy/dt-2 dz/dt=t^2

with initial condition y(0)=1, z(0)=2.

Thanks.

with(LinearAlgebra):

n := 31;

h := 0;

c1 := Array(1 .. 100);

c2 := Array(1 .. 100);

c3 := Array(1 .. 100);

for tt from 0 to n-4 do

c1[tt+1] := ...

c2[tt+1] := ...

c3[tt+1] := ...

od;

plot3d([c1[x],c2[x],c3[x]], x=1..27, y=1..27);

Here is the question:

Consider f(x)=x³ over [a,b] and a partition P of [a,b] into n equal subintervals. Find the length of this subinterval and assign it to dxj.

a) Assign the rightmost point of the jth subinterval to xj. Set up an expression corresponding to the Riemann sum for this partition with  as the rightmost point xj in each subinterval.

b) Find the limit of this expression as n->∞. Integrate f(x) between a and b and comment on your evaluation of the integral and the value of the limit.

 d) Show that the limit of the Riemann sum remain unchanged if

xj = the left most point in the jth interval

or if

xj = the midpoint in the jth interval

anyone know how to go about this question? thanks

I am trying to find what values of x f(x) is increasing without estimating from the graph