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**mrpace**- Replies: 1

Convert

F(x,y,z) = k / (x^2 + y^2 + z^2)^2

into spherical coordinates.

Thanks for the help.

Nehushtan wrote:

mrpace wrote:My answer is <0>, <12>, <20>, <32>

Is this correct?Looks good to me. As a subgroup of the given group, <32> = <4> is cyclic of order 15, and a cyclic group of order 15 has precisely four subgroups.

Thanks mate.

**mrpace**- Replies: 7

My answer is <0>, <12>, <20>, <32>

Is this correct?

**mrpace**- Replies: 1

Suppose that a, b, and y are all functions.

If ay=by and y is one-to-one and onto, prove that a=b.

This looked very straightforward at first then I realised that a and b are functions, not values. I am therefore stuck on what to do.

Any help is much appreciated.

**mrpace**- Replies: 1

For which values of Z do the following series absolutely converge?

∑ (Z+1)^n / 2^n

The sum is from n=0 to infinity.

Thanks for any help.

**mrpace**- Replies: 1

z is the set where Re(z)<1 or Im(z-1) does not equal zero.

so my question is when they say ''or'', do they also mean the points that satisfy both sets or does ''or'' mean exclusive to one set?

**mrpace**- Replies: 2

Show that,

|1 − zw*|^2 − |z − w|^2 = (1 − |z|^2)(1 − |w|^2)

where z and w are complex numbers and z* is the conjugate of z.

Not very fluent with algebraic properties of these things so please help!!

Thanks.

**mrpace**- Replies: 2

So according to my textbook

|iz*/2 - i/2| simplifies to |z-1|/2

where z* is the conjugate of z.

I can't work out how they got that so could someone please show it to me.

Thanks.

**mrpace**- Replies: 1

Suppose that f is continuous on the closed interval [a, b], a < b, and that f(a) =

A, f(b) = B, A < B.

Suppose further that f is strictly increasing on [a, b] (i.e. for any x1, x2 ∈ I, x1 <

x2, impliesf(x1) < f(x2)).

Let C be a number between A and B. Show that there is exactly one value of x in

(a, b) such that f(x) = C.

I used the bisection process to try to explain why this must be the case but i'm not convinced that's what they're looking for....any ideas???

**mrpace**- Replies: 1

Let X0 = 1, X1 = 1, and suppose that, for n ≥ 1,

Xn+1 = Xn + Xn-1(r^r)

where 0<r<1

prove by induction that....

Xn+1 ≤ (1+r)(1+r^2).......(1+r^n)

I've done several induction problems before, but this one has got me stuck.

Help is much appreciated

**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.