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**mrpace**- Replies: 1

For any real number c and any set S ∈ R, we define c + S to be the set {c + x : x ∈ S}.

Prove:

If a set S ⊆ R, and c is any real number, the c + S has a supremum and

sup(c + S) = c + sup S.

Any help is much appreciated, thanks.

**mrpace**- Replies: 1

I understand that if a sequence converges to a particular value then we call that sequence convergent.

However, what if the sequence converges to 2 values?

For example the sequence 2/3, -3/5, 4/7, -5/9 approaches -0.5 from below and approaches 0.5 from above. Do we just say that the sequence diverges?

**mrpace**- Replies: 1

Z[√7] = {a+b√7|a.b ∈ Z}

2Z+iZ = {2a+bi|a,b ∈ Z}

Where C is the complex plane, Z is the set of real integers.

Any ideas? Thanks.

**mrpace**- Replies: 0

Solve:

2y∂u - 3x∂u + 2xyu = xy

∂x ∂y

given that along Y^2 = (-1/2)x^2

u = 1/2 + cos(x)e^(x^2/2)

Any idea?

**mrpace**- Replies: 2

Find a permutation group isomorphic to U(16), X16

using the proof of cayley's theorem.

Any ideas?

**mrpace**- Replies: 2

Let H be the subgroup of all rotations in Dn and let φ be an isomorphism from Dn to Dn. Prove that φ(H) = H

Any ideas on this one?

**mrpace**- Replies: 0

Find the Green's function for the problem.

y'' - y = f(x) x>0

y'(0) = 0 lim as x goes to infinity of y(x) is 0.

Any idea on this one?

**mrpace**- Replies: 1

Find all the real eigenvalues and eigenfunctions for the eigenvalue problems

y'' + λy = 0,

y(-3) = y(3),

y '(-3) = y '(3).

Not really sure on the process. Thanks for any help.

**mrpace**- Replies: 10

Show that 5n+3 and 7n+4 are relatively prime for all n.

I'm fairly new at proofs and I think I've made decent inroads but can't seem to finish it elegantly.

Here is my attempt:

Show that gcd (5n+3 , 7n+4) = 1

let A=5n+3 and B=7n+4

if n is even then A is odd. If n is odd then B is odd. Therefore gcd cannot be even.

For an odd number (k) to divide A as well as B, the difference between A and B must be some multiple of k which can only be true if k equals 1.

That last line I don't think is sufficient but I don't know how to put it in more convincing terms. Help is appreciated.

**mrpace**- Replies: 1

Hey. I can find nothing on this material in my textbook and nothing online that's quite like it, so i'm hoping someone here can show me how to do this.

Consider the system

dx/dt = 4x + 5y + xy

du/dt = x + x^2 - y^2

Discuss the type and stability of the critical point at (0,0)

**mrpace**- Replies: 4

write the system

x'(t) = -3x(t) +y(t) +e^t + 1

y'(t)= 2x(t) - cost

In the matrix form x' = Ax + f

could this really be so simple as x' = {-3, 2}x +f ??

or is there more to it?

**mrpace**- Replies: 0

determine the laplace transform of f(t) of the following

f(t) =

e^(-t) when 0 ≤ t ≤ 5

-1 when t > 5

I got my answer as simply 1/(s+1) when 0 ≤ s ≤ 5

-1/s when s > 5

I'm not sure if this is right though.

**mrpace**- Replies: 1

Find all real values of a and b such that the following is a reflection

T: X = aX + (24/25)Y

Y bY + (24/25)X

Sorry for the lack of latex; I'm sure you can work it out.

Agnishom wrote:

There is no need to factor it. You are confusing yourself by factoring it

Really? I'm trying with it not factored and not having any luck.. can you help?

**mrpace**- Replies: 3

show, using the formal definition of a limit, that:

lim

x^2=4

x -> 2

I'm getting to a point where I have |x+2||x-2| < E

But I don't know where to go from there. Help is much appreciated.

**mrpace**- Replies: 1

Find a sequence of plane rotations that transform x = [6 6 17] to a multiple of [1 0 0].

Any ideas??

**mrpace**- Replies: 3

Show that if A and B represent reflections in R3, then AB represents a rotation in R3.

Any help is appreciated.

**mrpace**- Replies: 1

A force of 400 N stretches a spring 2 meters. A mass of 50 kg is attached to the

end of the spring and is initially released from the equilibrium position with an

upward velocity of 10 m/s. Find the equation of motion

My answer is x=5sin(2t)

If youu get something different, can you show me how you got it please?

Cheers.

**mrpace**- Replies: 2

Find a general solution to

y′′′ − y′′ + 2y = 0

I have never dealt with 3rd order D.E before. I hope you have!

**mrpace**- Replies: 1

Given that y1 = x^(-2) , find a second linearly independent solution to

(x^2)y′′ + 6xy′ + 6y = 0, x > 0.

Any help would be much appreciated.

Hey that's really nice. Just one thing. How would you say in English min{d1,d2,d}?

and i see where the d1 and d2 come from in the brakets above, but where does the d come from??

d=delta obv.

**mrpace**- Replies: 3

Prove that if lim f(x) = lim g(x) = b, and if there exists a number δ > 0 such that...

x→a x→a

0 < |x − a| < δ ⇒ f(x) ≤ h(x) ≤ g(x)

then lim h(x) = b.

x→a

Worked on this for a while without getting anywhere. Any ideas???

**mrpace**- Replies: 8

If f(x) = ax + b for all real numbers x, where a and b are numbers, find for what values

of a and b is it true that ff = f o f?

Not sure what it means by ff or f o f. Help is much appreciated.

bob bundy wrote:

hi mrpace

Because the definition comes in two parts, the answer will too.

x ≥ 0 :

x < 0

You could argue that f(0) is undefined when x < 1 and therefore this second answer cannot be determined but I don't think that is intended.

I have used Latex. If you click on the expression above you'll get a window that shows the code for this. You have to add at the start square brackets math, and complete the code with square brackets /math

Thus:

`[math]\frac{h^2 - 0}{h} = \frac{h^2}{h} = h[/math]`

There's a tutorial to get you started here:

http://www.mathisfunforum.com/viewtopic.php?id=4397

The first few posts in that thread will be enough to get you started. There's an editor at:

http://latex.codecogs.com/eqneditor/editor.php

Bob

Great. I see how it works now. Thanks a lot.

**mrpace**- Replies: 2

If f(x) = x^2 if x is greater than or equal to zero.

= 1 if x is less than zero

then find an expression for the following:

[f(h) - f(0)] / h

h can't equal zero obviously

I don't know how to do these problems so any help is appreciated.

Sorry for the lack of latex...i tried to learn but i don't get it.