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Hi everyone,

I've been having a problem with this question:

"The system of cities and roads in Connected Graphs on page 246 splits naturally into two components: the Canadian cities and roads between them, and the European cities and roads between them. In each component you can travel between any two cities, but you cannot travel between the two components. Write a procedure that, given a table of neighbors, splits the system into such components. Hint : Think about the form in which the procedure returns its result."

I have to separate a table into two tables based on the connectivity of the cities, that is, I want a table just for the cities from Canada and another one for the cities from Europe. Can anyone help me with this? I really have no idea how to tell Maple what I want it to do.

Anyway, here's the link with the soon-to-be program:

6.9.mw

The algorithm that I need to replicate is as follows:

real function f(x,y)

integer n; real a,b,c,x,y

f<-max(|x|,|y|)

a<-min(|x|,|y|)

for n=1 to 3 do

b<-(a/f)^2

c<-b/(4+b)

f<-f+2*c*f

a<-ca

end for

end function f

How can I define f,a as  functions that I am later using as variables(in f=f+2cf,b=(a/f)^2)? also, is n just a variable for iteration? 

 

I've got a function f(x_n) = (x_n-1)^3

and need to show that for the iterative method

x_(n+1)= x_n - f(x_n)/(sqrt(f'(x_n)^2-f(x_n)*f''(x_n), at a simple root we have cubic convergence while at a multiple root, it converges linearly.

I understand that the approach is to write either a recursive function or a sequence, but i'm confused about the structure since both x and n are being incremented

 

I need to show what happens to the zero r=20 of f(x)= (x-1)(x-2)..(x-20)-(1/10^8)*(x^19) and the hint given is that the secant method in double precision gives an approximate in [20,21].

At present, I'm calling the secant method on f with a tolerance of 1/(10^12) with an initial x=20, but I'm stuck as to what the second initial value would be. What is the right approach to this question?

 

I've plotted the graph for this max function. Is there any way I can find the points of discontinuity in general and then use that to compute the derivatives at points where it exists?

Hello, I need a person who can help me with task from numerical methods.

I need to convert a base 10 int(defined as num) to its base 3 format using a while loop. I would like to store the remainder of the num%3 to a list/sequence/array in maple. Now, if I were to use a sequence, I would need a pre-defined range. How do I solve this issue?

I have to find the volume of a solid using the disk/washer method and the shell method.  I think I have the first part(disk/washer) right.   I think the shell is off. The problem is "the region in the first quadrant that is bounded above by the curve y = 1/x^1/4, on the left by the line x = 1/16, and below bythe line y = 1 is revolved about the x-axis to generate a solid."    I am having computer problems so any help is appreciated. Thanks

A 37 foot ladder is placed against a wall that is 9 feet away from its base. Will the top of the ladder reach a window ledge that is 35 feet above ground? Explain.

True of False, Explain:

If ∏/2<θ<∏, Then cos θ/2<0

The problem is The square root of 16-x^2 over the interval [0,-4]  0 being the upper bound, -4 being the lower bound.  I have solved 3/4s of this problem but I don't understand what they mean by "Solve the definite integral exactly by geometry". 

Is there a way to do the following on Maple:

I want Maple to use Jacobi's method to give an approximation of the solution to the following linear system, with a tolerance of 10^(-2) and with a maximum iteration count of 300.

 

The linear system is

x_1-2x_3=0.2

-0.5x_1+x_2-0.25x_3=-1.425

x_1-0.5x_2+x_3=2

 

Thanks.

Egor has two parents, four grandparents, and so on.
Write an explicit formula and a recursive formula for the number of ancestors Egor has if we go back n generations.                

what would be the figure back to 25 generations ?

Let (G, ·) be a group and X any set. Let F be the set of functions with domain

X and range G. Define a binary operation ∗ on F by (f ∗ g)(x) := f(x) · g(x). Is

prove that this is so.

Yes, (F, ∗) is a group.

prove it.

Exercise Prove that (-1)u = - u in any vector space. Note that (-1)u means the number -1 is multiplied to the vector u, and - u means the negative vector in the fourth property of the definition of vector spaces.

Answer

Exercise Prove that (a1u1 + a2u2) + (b1u1 + b2u2) = (a1 + b1)u1 + (a2 + b2)u2 in any vector space.

Answer

Exercise Give a detailed reason why, in any vector space,

  • u + v = 0 ⇒ u = - v.

  • 3u + 2v - 4w = 0 ⇒ v = - 3/2 u + 2w.

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