Reciprocal Definition and 166 Threads

Given the following graph: http://img245.imageshack.us/img245/2395/scan0001ou4.gif How can i sketch the reciprocal of that function? There are poles at x=-2 and x=2, so it means its reciprocal will have roots at -2 and 2 right? But that's not really enough information to compose a full...

Consider the series with ascending (but not necessarily sequential) primes pn, 1/p1+1/p2+1/p3+ . . . +1/pN=1, as N approaches infinity. Determine the pn that most rapidly converge (minimize the terms in) this series. That set of primes I call the "Booda set."

Question 1 — Construct the crystal lattice from the diffraction pattern drawn on page 5 of this exam paper making sure you include the (110) and (220) planes. Explain the procedure used in reconstructing the crystal lattice. What Bravais lattice is represented by the diffraction pattern...

I know this might be a really stupid question, but to convert a crystal lattice 2D representation to a 2D reciprocal lattice do you justdo you just invert the scaling. I know this is a pretty poor explanation so I will try and illustrate what I mean. Let's say that you have a reciprocal lattice...

How do I show that \sum_1^n\frac{1}{k} is not an integer for n>1? I tried bounding them between two integrals but that doesn't cut it. I know that \sum_1^n\frac{1}{k}=\frac{(n-1)!+n(n-2)!+n(n-1)(n-3)!+...+n!}{n!} but I can't get a contradiction.

If we are studying FCC in the direct lattice, Why does the length of the cube side in the reciprocal lattice equal to 4*Pi/a Where a is the lattice constant, a*=|G|=2*Pi/a Sqrt(4) = 4*Pi/a Where a* is the length of the cube site in reciprocal lattice Note: this thing is repeated in 2...

Suppose a_n is a bounded sequence. Then prove that lim sup a_n = 1/lim inf (1/a_n). This seems completely obvious to me, I don't know how to do this any simpler.

Hi I have a proof I'm doing \int \frac{1}{1+\sin(x)}dx I know that the answer I'm looking for is \frac{\sin(x) - 1}{\cos(x)} and then \tan(x) - \sec(x) I have tried integration by parts making u = (1+\sin(x))^{-1} and dv = dx Eventually I get an answer that...

I am to find the imaginary part, real part, square, reciprocal, and absolut value of the complex function: y(x,t)=ie^{i(kx-\omega t)} y(x,t)=i\left( cos(kx- \omega t)+ i sin(kx- \omega t) \right) y(x,t)=icos(kx- \omega t)-sin(kx- \omega t) the imaginary part is cos(kx- \omega t) the...

What is an equation of a relation that appears to be its own reciprocal? :rolleyes:

If two resistors with resistances R1 and R2 are connected in parallel, then the total resistance Rt, measured in ohms, is: \frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} If R1 and R2 are increasing at rates: \frac{d \Omega_1}{dt} = 0.3 \; \; \frac{d \Omega_2}{dt} = 0.2 \; \; R_1 = 80 \...

can any1 explain why this iteration: Xn+1 = Xn(2 - NXn) can be used to find the reciprocal of N. I don't ned proof or to show that it does but i would like to know if sum1 can break it down and explain how it does it.

Compute the following: \sum_{n=1}^{+\infty} \frac{1}{n^{2}} =...?? \sum_{n=1}^{+\infty} \frac{1}{n^{4}} =...?? .LINKS TO WEBPAGES WITH SOLUTIONS ARE NOT ALLOWED! :-p Daniel.

The terms of this series are reciprocals of positive integers whose only prime factors are 2s and 3s: 1+1/2+1/3+1/4+1/6+1/8+1/9+1/12+... Show that this series converges and find its sum. this is my first time writing here. i hope someone can help me with this question.

Er well I've been away from math for a LONG time until I recently began reading into calculus and I have a question. I always see reciprocal and inverse throughout the text. What is the difference between the two? I always thought reciprocal was the number (in a fraction form) flipped so...

A triangle in Euclidean space can be described as having a hypotenuse of one, and legs of Lorentz parameters \beta and \gamma. What spatial curvature underlies a triangle with hypotenuse one, and legs 1/ \beta and 1/ \gamma?