Recent content by Easty

Thank you Hallsofivy. Once i took your advice the answer was quite simple to obtain, it was a nice way to approach the problem that i would have never seen.

1. Homework Statement [/b] f _{a} (z) is defined as f(z) = 1 + az + \frac{a(a-1)}{2!}z^{2}+...+\frac{a(a-1)(a-2)...(a-n+1)}{n!}z^{n} + ... where a is constant Show that for any a,b f _{a+b} (z)= f _{a}(z)f _{b}(z) Homework EquationsThe Attempt at a Solution I've tried starting directly...

Try guessing the form of the wavefunction to be \Psi=exp(ikx)Y(y)Z(z) Once you substitute this into your equation you should be able to decouple the motion in the y direction and the exp(ikx) terms should cancel.

I think I've got it na^2 >= 0 add 1+(n+1)a to both sides 1+(n+1)a+na^2 >= 1+(n+1)a therefore (1+a)^(n+1) >= 1 + (n+1)a + na^2 >= 1 + (n+1)a (1+a)^(n+1) >=1 + (n+1)a as required i'm pretty sure this is correct. Thanks for all your help lanedance

i had gotten to that stage, but thought it led no where. The only term that isn't part of the original equality is na^2, since a is >-1, a^2 >= 0, so couldn't the extra term add some arbitary large positive number such that the inequality wasnt true?

Homework Statement Using mathematical induction, prove the inequality (1+a)^n >= 1+na for all a>-1 and all n Homework Equations The Attempt at a Solution Base case 1+a >= 1+a. the inequality holds. I am struggling with the inductive step. by working backward, i multiply...

Ok thanks. So would the solution of the PDE still be just an arbitary function of the constant combination of variables? how do i combine all the characteristics to form a single solution?

b]1. Homework Statement [/b] Find the characteristics, and then the solution, of the partial differential equation x\frac{\partial u}{\partial x}+xy\frac{\partial u}{\partial y}+z\frac{\partial u}{\partial z}=0 given that u(1, y, z)=yz Homework Equations The Attempt at a...

you would have to use both parts of f(t) when finding an and bn. all you need to do is break up the integrals that determine an and bn to the appropriate domains for each part of your function.

but then arent you assumeing that h(x)= h_2(h_1(x)) is a contration?

Homework Statement If h1 and h2 are contractions on a set B with contraction constants δ1 and δ2 prove that the composite function h2 ° h 1 is also a contraction on B and find a contraction constant. Homework Equations |f(a) - f(b)| ≤ δ |a-b| f '(c) = (f(a)-f(b))/(a-b)...

Why is it that you can get sine and cosine solutions? i thought all you needed was the sine solution because it would always satify the boundary conditions of haveing a node at each boundary.

Ok then so it must be C=(0, 3). As for part b would this sequence work: (1/n*sin(n)). It should converge by the absolute convergence theorem i think. I'd appreciate any comments or criticisms. thanks

Hi Pyroadept Its probably worth mentioning the associated force in each situation, and how the force is created. After all its the force that causes the wire and magnets to move in the first place.

Homework Statement Let C=\bigcupn=1\inftyCn where Cn=[1/n,3-(1/n)] a) Find C in its simplest form. b)Give a non-monotone sequence in C converging to 0. Homework Equations The Attempt at a Solution For part a) i get C=[0,3]. Is this correct? I am not sure as to wether 0 and 3 are...