Natural Definition and 1000 Threads

I'm puzzled by... \ln \left( -\frac{1}{2} \right) = - \ln \left( 2 \right) + i \pi Why is this true? How can I possibly get this result? I know that \ln \left( \frac{1}{2} \right) = - \ln \left( 2 \right). Thank you so much

Lets take an electron which is "in orbit" around the nucleus. As far as I know, its (ANY conceivable) wavefunction can be represented as a superposition of energy eigenfunctions, which correspond to the discrete eigenvalues of the electron's enrergy. What I do not understand is where the natural...

Hello all If y = e^3^\ln^(x^2) find \frac {dy}{dx} So \frac {dy}{dx} =(3 (\frac {1}{x^2}) \* 2x e^3^\ln^(x^2) So the simplified answer is: \frac {6}{x} e^3^\ln^(x^2) Is this correct? IS there any other way of expressing the answer? Thanks

Hi everyone! (d/dx) [xlnx] Why is the answer 1+lnx and not 1?? ~Thanks

Quick! Read this before it goes into Nature's archive and no longer becomes free. http://www.nature.com/news/2004/041220/full/041220-12.html Zz.

NEMS Resonator I need a hint to help with my homework. The question: "A Si-Based NEMS resonator has dimensions length=150nm, width=5nm and thickness=5nm and an effective spring constant of 100Nm^-1 and natural frequency of vibration of 250MHz" I am looking for an equation linking the...

Besides manmade lasers, from what phenomenon might the coherent light of naturally occurring lasers originate?

Hi Guys, i am new to this forums and my english is poor, but i will do my best. I got stuck with this problem, i think it's quite easy, but i get the wrong answer :frown: F(x) = ln(1+e^x) 1. Show that it has an inverse 2. What is the Range And the Domain of the inverse. I really...

e^{-x^2}=(e^x)^3(\frac{1}{e^4}) Wouldn't all the Es cancel out? -x^2=3x-4 Move the 3x and factor out a -x: -x(x+3)=-4 Now I got nothing.

Please Help! Natural Log Question! Here is the question that is bothering me: I need to solve this natural log for x. Please I need step by step instructions on how to figure out x. Thanks very much. ln (x) + ln (x+1) = 2

is global warming a natural phenomenon? I think it is . But we can enhanced it such as we produce tonnes of carbon dioxide every day, causing the greehouse effect strengthen and finally lead to global warming .

I tried induction, but got no results. What I get is: f(n+1) = 4f(n) - 6f(n)/(n+2) So now I'd have to prove that 6*(2n)!/[n!(n+1)!(n+2)] is natural, which would be going in circles. I tried to go directly, but came up with nothing good. It can be written as [2n over (n-1)] / n, but I...

i suck at science can n e 1 help? what is the natual state of plutonium?

Hi, I need some help! :rolleyes: I have a series of maths problems in my physics work... I am trying to integrate a power of a log - such as: y= 3.2875E+004 - 8.9321E+005*ln x + 4.2316E+006*(ln x)^2 - 7.7776E+006*(ln x)^3 + 7.4949E+006*(ln x)^4 - 4.1373E+006*(ln x)^5 +...

Here's the problem: find the integral of dx/2x(lnx)^1/2 In other words, dx over 2x times the square root of lnx. It has to be evaluated from 16 and 2. I don't know how to say it, but the integral sign with 16 at the top, and 2 at the bottom. If you can find the answerm and show me...

[SOLVED] Integration of a natural log I am asked to Integrate by parts \int \ln(2x+1) dx So, \mbox{u}=ln(2x+1) \mbox{du}=\frac{2}{2x+1} \mbox{dv}=\mbox{dx} \mbox{v}=\mbox{x} I plug all of that in and I get, {\int \ln(2x+1) dx\}={\mbox{x}\ln(2x+1)}-{\int \frac{2x}{2x+1}...

I have a tour coming up of the western mainland of the USA, starting in California. I've already seen those large groovy canyons. What else is there to see over there, in terms of natural scenery? I hear the Rocky Mountains look quite nice, and it's not far out of my path. Any suggestions?

I remember I used to be sad when I saw an animal die, especially if it were something like a domesticated cat catching a chipmunk and not even eating it. I was always aware of natrual selection, but it was never at the forefront of my mind when thinking about this, I always thought that it was...

can anyone let me know where to get more info about natural language? tks

Are sine waves the waves that are theoretically deemed to be the waves [naturally] emitted by all matter? Or am I getting them confused with something else?

Umm I hear that some scientist often get together with architects and engineers to discuss the importance about having windows to allow natural sunlight to enter. I heard it was discovered that natural sunlight actually helps in the slow process of creating new brain cells. Is anyone familiar...

For your amusement. For obvious reasons I assume this is completely bogus. http://www.amasci.com/greb/greb2.html

i need help with this one question; we have to write ln9-3ln(squareroot 3) + ln81 in the form kln3 where k is an exact fraction; i don't remember how to do this at all so any help would be greatly appreciated; thanks

Problem 51. At a constant temperature, the atmospheric pressure p, in pascals, is given by the formula p=101.3e^-0.001h, where h is the altitude in meters. Find h when p is 74.3 pascals. Hint: Start by taking the natural logarithms of the expressions on each side of the equation. Solve and...

where can I find data about the natural vibration of differrent materials ?

where can I find data about the natural vibration of differrent materials ?

what is the result or simplification of ( ln(i^2) )^2 sweet bro :confused:

I am having trouble with some homework on natural deductions. I just don't know how to approach the problems. For example, one problem is to show that irreflexivity and transitivity imply asymmetry. Any strategies on how to reason the deductions would be great (the rules are simple enough...

This law neither I can prove right nor you can prove wrong. This law leaves as trully neutral. The law is:"Displacement always takes the direction of the force causing it" It's the compromise between Newton 1 and Newton 2.

I'm trying to figure out how to do this problem... Solve for x: \frac{e^x-5e^{-x}}{4}=1 I know the answer is ln(5) [given by both the book and TI-89 calculator], but I can't figure out why.

In semi-response to Organic's post I thought I'd half take up one of his challenges: Let S = NxT be the product of the natural numbers, N, with the set of all rooted finite trees (or directed graphs satisfying the obvious conditions), embedded in the plane, with the natural ordering on the...

Sherman Hawk, The Book of Millennium If it be the truth that human beings, as biological organisms, are subject to the natural laws which govern other creatures, then surely it is also true that human beings, as a species, hate themselves. The one thing which has made us great, we undermine...

I would greatly appreciate if someone just at least put me in the right direction with this. I have to prove this: Prove that of a,b,c are natural numbers, gcd(a,c) = 1 and b divides c, then gcd(a,b) = 1.

If set A consisted of all even natural numbers (i.e. 2, 4, 6...) and set B consisted of all odd natural numbers (i.e. 1, 3, 5...), then what is the result set of: A intersection B Would it just be the empty set since no two natural numbers can be even and odd?

Hi, I am still having trouble with taking the integral of the following: integral of ln(x+1) dx I am trying to do it by parts but I end up getting stuck. I had no problem doing: integral of ln x dx But I can't seem to get integral of ln (x+1) dx Let u = ln (x+1) then du =...

Hello, It has been over a year since I last took calculus. And I don't recall how to take the integral of a natural logarithmic function. Here is the question that I am supposed to integrate. double integral 1/(x+y) dA where R = [1,2] X [0,1] So what I did first was integrate...

I have heard that non-cohesive surface contact is such that any given "object1" is floating on "object2" in the sense that there is a separation, however small, due to electron repulsion. When I pick up my coffee cup, under this theory, my fingers never actually touch the cup, rather interact...

INT x^(1/3) / x^(1/3) -1 dx u = x^(1/3) x = u^3 dx = 3u^2du INT (u/u-1)3u^2du = 3 INT u^3/(u-1) du INT [u^2 + u + 1/(u-1)]du Then just integrate each part? ----------- Find the area of the region bounded. y=2x - tan(0.3x), x-1, x=4, y=0 Need some guidance where to start here...

Doesn't it just crack you up when a company will advertise their products touting "ALL NATURAL - NO CHEMIALS!" To me, this just flies in the face of reason. Let's see - Foxglove is all natural but it can kill you! And show me a flower that is NOT made of chemicals and I'll show you empty...

All the world needs is a dozen Phobos's

The National Inst. of Standards and Technology NIST has a fundamental physical constants website http://physics.nist.gov/cuu/Constants/ and until sometime this year what they posted were the 1998 CODATA recommended values (same as those in Physics Today August 2000, or the CRC Handbook of...

This is just a curiosity that I am confused about; is natural selection within human society still considered natural selection? I am confused in that people are no longer focusing on natural features so much as artificially "enhanced" features. Is an artificial enhancement resulting in...

Does anyone know a set of axioms for natural deductions? One which leads to the rest of the tautologies of the propositional calculus (and,or,not,if,iff) as theorems? I want the number of undefined logical operators to be limited to two, either {not,and} or {not,or}.

The problem I have is to find the derivative of the function: f(x) = (ln x)^x I know the derivative of ln x is 1/x, but the exponent is throwing me off. Can anyone offering any help? Thanks alot

is there a "brand logo" for natural science? I had posted an earlier version of this somewhere on this forum sometime ago, but in order as not to make things too easy for you, I'm now posting this thing again. So guess what this is! :smile: Whenever I watch movies like "Contact", or also in...

We know that the sum of the first n natural numbers is n(n+1)/2 Can we express the product of the first n natural numbers without using the factorial symbol? It is possible to write a factorial as a sum. Any idea what it would look like?

im still on the fence, is global warming natural or manmade? i don't know i have read that eruptions from mamalian rear ends has a lot to do with it how could one stop that. no crudidity intended.

How cool is this!? http://www.cnn.com/2003/TECH/08/21/natural.fiberoptics.ap/index.html

The following began on the thread How would you engineer the perfect human?, which I decided to continue on here. I thought it was unusual that everyone was talking about genetically altering human beings, and wondering what if anything it had to do with natural selection? For this would almost...

Is love of golf an inherited trait? Did it evolve as a response to the existential boredom that men experience, but women do not? I haven't done a scientific study, but thought I would pass on anecdotal results. Every time I play golf, I notice that the course is about 90% men (that would...