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## #1 Help Me ! » Proof to do with supremums. » 2015-07-28 03:25:07

mrpace
Replies: 0

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.

## #2 Help Me ! » Quick question on sequence convergence. » 2015-07-23 05:57:29

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?

## #3 Help Me ! » Which of the following are subrings of C? » 2015-05-12 14:49:21

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.

## #4 Help Me ! » Solve the following differential equation. » 2015-04-12 18:04:14

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?

## #5 Help Me ! » Find a permutation group isomorphic to.... » 2015-03-26 02:32:33

mrpace
Replies: 2

Find a permutation group isomorphic to U(16), X16
using the proof of cayley's theorem.

Any ideas?

## #6 Help Me ! » Question on isomorphisms » 2015-03-26 02:09:26

mrpace
Replies: 0

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?

## #7 Help Me ! » Find Green's function for the problem... » 2015-03-22 12:20:47

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?

## #8 Help Me ! » Differential Equations help please » 2015-03-20 15:51:55

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.

## #9 Help Me ! » Help with a fairly simple proof please? » 2015-02-24 21:53:32

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.

## #10 Help Me ! » Critical points problem: Differential equations » 2014-10-13 17:35:13

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)

## #11 Help Me ! » Differential equations problem » 2014-10-01 01:13:20

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?

## #12 Help Me ! » Help with Laplace transform please » 2014-09-15 16:47:11

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.

## #13 Help Me ! » Linear Transformation problem » 2014-09-11 14:06:37

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.

## #14 Re: Help Me ! » Prove this limit » 2014-09-11 03:01:03

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?

## #15 Help Me ! » Prove this limit » 2014-09-11 02:01:47

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.

## #16 Help Me ! » Help with plane rotations?? » 2014-09-10 16:11:36

mrpace
Replies: 1

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

Any ideas??

## #17 Help Me ! » Linear algebra help?? » 2014-09-09 14:02:29

mrpace
Replies: 3

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

Any help is appreciated.

## #18 Help Me ! » Check my answer please » 2014-08-16 16:35:19

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

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

## #19 Help Me ! » General solution for this differential equation?? » 2014-08-16 12:48:30

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!

## #20 Help Me ! » Help with differential equation problem please » 2014-08-16 12:44:52

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.

## #21 Re: Help Me ! » Challenging proof. » 2014-08-14 00:04:27

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.

## #22 Help Me ! » Challenging proof. » 2014-08-13 21:49:20

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.

## #24 Re: Help Me ! » Help with this weird question?? » 2014-08-11 22:32:24

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:

  $\frac{h^2 - 0}{h} = \frac{h^2}{h} = h$

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.

## #25 Help Me ! » Help with this weird question?? » 2014-08-11 16:48:25

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.