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Find the Fourier Series for the function f(x) defined as follows, and compare the graphs of some truncated Fourier series (try 1,2,3,5,6,30, terms) with the graph of f(x).


f(x)= min(|x|, pi/2), -pi less than or equal to x less than or equal to pi.


Also, let f(x) be periodic with a period of 2*pi. Thanks.

4(x-7) =6



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


Ive been given a task to write a fuction that will print true/false to if a given line will intersect a triangle given the co-ordinates of the vertices. 
I have a general idea on what needs to be done mathmaticly, but i have poor maple skills and the syntax is killing me.
I would appreciate some help in this regard.



Ok so my problem is that I need to write a function which produces the three inequalities defining a triangle given the 3 points that form its vertices, then with the 4th point supplied to the function I need the function to print false if the 4th point satisfies less than 2 of these inequalities and true if it satisfies more than 2 of these inequalities. Can anybody help me with this? On a previous post I obtained part of the function that produces the triangle, but the 2 inequalities part was not solved.

Thanks for your time


  1. 1.    The bending moment M, in a simply supported beam is represented by the formula: (5marks)


 M = w x/2 (l-x)


Where: w = uniformly distributed load in KN per m

            x = distance from the left hand end of the beam in m 

            l = span of the beam in m 



If  = 4KN per m and  = 5m, calculate the value of  where  = 12KNm


Any thoughts on this guys? 

I know this is cheeky but i was wondering if there was anyone out there that would be willing to pretty much do this question for me? i have been at this all night and still not the slightest clue. Any help would be much apprefiated. 


  1. 1.    Below are 4 questions that require solving problems by formulating simultaneous equations. Solve each question and explain the method you used. What other methods could be used other than those you have used to solve here. (total 30 marks)

(a)  A penalty clause states that a groundwork’s sub-contractor will forfeit a certain sum of money for each day that they are late in completing a contract (i.e. the sub-contractor gets paid the value of the original contract less any forfeit). If they are 6 days late they receive £5000 if they are 14 days late they receive £3000. (8marks)

  1. a.    Find the amount of the daily forfeit
  2. b.    Determine the value of the original contract.

(b)  The total cost of purchasing 2 excavators, A and B is £30,000. The 2 tonne excavator costs £2,000 more than the 1.5 tonne excavator. Find the individual cost for each excavator. (7marks)

(c)  You are estimating costs for a heat recovery installation. You know that 100m of 100mm dia ducting and 8 bends cost £100 and 150m of 100mm ducting and 10 bends cost £147.50. Find the cost for 1m of ducting and 1 bend. (8marks)

(d)  You are a Site Manager who is organising a lift utilising a tower crane you have on site. You know that the Force (F) in Newtons required to lift a load (W) in Newtons is represented by the equation F = aW + b. You know that a force of 100N lifts a load of 180N and a force of 150N lifts a load of 280N. Find the values of a and b and the force required to lift a load of 500N. (7marks)

Dear Maple forum,


given A, B real numbers,

and after defining the recurrent sequence


x(0) = A

x(n) = 0.5* x(n-1)^3 + B


I would like to see a graphic of x(n) on the plane x(n) - n.

how could I implement in maple 16?


thank you for your help.



  1.   The formula to calculate a length of rafter may be given as

Length of rafter = √ (rise)squared + (run)squared            

      (The whole of the RHS has been square rooted but cant type that symbol)

Transpose this equation and express in terms of the rise. Describe each stage so as to clearly identify what you have done.  Using this new equation calculate the rise if the length of the rafter is 7m and the run is 6. Write your answer to 3 s.f. 



If anyone has any ideas or could help it would be really appreciated. Thanks. 


I don't know how to write a function that determines whether a non-zero vector intersects a triangle with given vertices. If anybody could help me write a function that satisfies this so that the function returns true if the vector spanning the line intersects the triangle and returns false if it doesn't I would be greatly appreciative.

okay so i have to write a maple function that decides wheter a line given by a vector that spans it intersects a triangle with given vertices. 

an example of what it should look it is 

ISC([[0,0],[10,10],[10,10]],[2,1]) returns true

ISC([[0,0],[10,10],[10,0]],[-2,1]) returns false


thanks in advance.  i'm just having severe problems with writing functions and what not as you can tell. anyway, Thanks!!

okay so the question i have to answer is "write a maple function that computes the area of a triangle in the plane from the coordinates of the vertices"  

ive gotten this far 



triangle(ABC, [point(A, 0, 0), point(B, 2, 0), point(C, 1, 3)]);

area(ABC);    3


but how can i write so when you type say AA([[0,0],[10,10],[10,0]])  it returns  50?  (AA being the function name)


Thanks in advance to whoever helps.


New to maple and I have 2 questions that I'm stuck on.


1) Find the principal arguments of the 5 roots of the polynomial

and enter a decimal approximation to the largest principal argument in the box below.

ans: 2.589502038


2) Find the moduli of the 5 roots of the polynomial

and enter a decimal approximation to the largest modulus in the box below

ans: 2.34880159160143


I dont really know what to write in maple to get the answer. So, if someone could help me out that would be really great. cheers





This is what i have done to find the difference between a ball thrown with different starting angle, and then ploted they into the same plot.

restart; Digits:=20: with(plots):

C_0:=0.4: d:=0.0002: mu:=1.8*10^(-5): rho:=1.2: g:= 9.81:
rho_v:=1000.0: m:=evalf((4/3)*Pi*rho_v*(d/2)^3):   

local k,vx,vy; 

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