Natural Definition and 1000 Threads

I'm having real problems integrating a natural log. The problem I have been set is (where S = integration sign) S (x - 2) Ln(3x) I'm trying to use the integration by parts rule but keep getting the wrong answer and I think it might be to do with the natural log. I have used f(x) =...

If we have a function of the form Ln(ax) Is it the case that the derivative is simply 1/x no matter what the initial value of 'a' might be? Or do we take into account 'a' in some way The thing i need clarifying is this... If we have Ln(3x), the derivative is 1/x, but the integral of...

What event creates and sustains natural electromagnetic fields? And what do they mean when they say a photon mediates the electromagnetic field?

Homework Statement the indefinite integral of (1+lnx)^(1/2)/(xlnx) dx Homework Equations n/a The Attempt at a Solution There aren't any x^2 in the root sign, so I don't think it can be a trig substitution. The only logical u sub I see is to let u=lnx. In that case, du=dx/x so the...

Hello everyone, I do not understand how:: e raised to ln of x = x ? this notation might make more sense:: e^ln x=x ? Thanks for the help.

I'm tired of hearing people like the skeptic Michael Shermer or James Randi talk about natural explanations for supernatural events. I believe that supernatural events are natural events that we are not advanced enough to explain. These events are true and we can deduce there truthfulness...

Hi, just can't get my head around how to draw these three graphs. Any help appreciated. Thanks In each case below, draw the graph of a function f that satisfies the given property. Give an example of a function f : N -> Z that is bijective/that is injective but not surjective/that is...

This is a new book from Cambridge University Press, scheduled to go on sale 30 June 2007, available now for pre-order https://www.amazon.com/dp/0521848415/?tag=pfamazon01-20 The Cambridge.org webpage for the book is here http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521848411...

Homework Statement Using a highly sensitive parabolic sound collector, Sara records the frequency of a tuning fork as it drops into the Grand Canyon. She drops the vibrating tuning fork form rest at t=0. She records a frequency of 1783.0Hz at t=8.590s. What is the natural frequency of the...

Do people usually prove that Z is an abelian group under (normal) addition or is it the definition of the natural numbers Z?

I was working on an experiment for the vapor pressure of water and I have the following formula ln (p) = -L/(RT) + ln (p_o) L=heat of vaporization of water R=Molar gas constant T=temperature in Kelvins I have some data points for the pressure p in units of mm Hg, when I take the...

Hello all, Another quick question for the number theory gurus here: Let P(n) predicate, n Natural number. Suppose that P(n) satisfies that P(1) is true, and if k in N, P(k) is true, then P(k+2) is true. Is P(n) true for ALL n in N? Why? Thanks in advace guys! -William

Homework Statement xln(2x+1)-x+\frac{1}{2}ln(2x+1) = \frac{1}{2}(2x+1)ln(2x+1)-xHomework Equations ln(x^a) = aln(x), ln(xy) = ln(x) + ln(y), ln(\frac{x}{y}) = ln(x) - ln(y)The Attempt at a Solution I have no idea how you can go from xln(2x+1)-x+\frac{1}{2}ln(2x+1) to...

Can someone explain to me when to use natural log or common log? I understand that natural log gives creates a base e and the common base 10 but i don't understand why there are 2 different ones.

Creativity...learned or natural (born-with) I had this conversation with some friends / coworkers today at lunch and both sides made good points. I'd like to get a view from everyone on these forums on the subject. I guess it all comes back to the big question you hear throughout management...

Homework Statement Reading about the raditation dominated era I saw that the radiation energy density today was given by: \rho_r = \frac{\pi^2}{30} g_* T^4 = 8.09 * 10^{-34} g/cm^3 where g_*=3.36 is the degree of freedom of the radiation (equivalent) and T=2.75 K is the CBR...

at least 10.. Thank You

I want to know whaqt chemicals can cause you to hallucinate naturally. DMT is released from The Pineal Gland and can cause hallucinations. Psychdellics are nothing more than substances that arouse and awaken the mind. They're awareness drugs. So I want to know is DMT the neurotransmitter that...

Homework Statement Prove that: 1^3 + 2^3 + ... + n^3 = (1 + 2 + ... + n)^2 for all n where n is a natural number Homework Equations Proof by induction: a) p(1) is true b) assume p(k) is true then prove p(k+1) for it The Attempt at a Solution I gave this a try for a while but...

Homework Statement find dy/dx for y=ln(sec^(2)x) Homework Equations none The Attempt at a Solution 1.)1/(sec(x)^2)*dy/dx sec(x)^2 2.)tan(x)/sec(x)^2 3.)i put it in terms of sin and cos... sin(x)/cos(x)*cos(x)^2/1 4.)i canceled the cos(x) in the denominator and came...

The status of cosmological natural selection Lee Smolin 25 pages "The problem of making predictions from theories that have landscapes of possible low energy parameters is reviewed. Conditions for such a theory to yield falsifiable predictions for doable experiments are given. It is shown...

I have the problem 3e^(x+2) = e^(-x) and I need to find X. It's been a while since I've looked at any Calculus 2 stuff so I am not sure on what to do here. I take the natural log of both sides LN(3e^(x+2) =LN(e^(-x))= (x+2)ln3e = -xlne So (x+2)Ln3e= -x Where do I go from here?

Homework Statement OK I haven't been given a definite question with values, but how would you find the natural frequency of a system of two pendulums coupled by a spring? Homework Equations a= -gx/l T=2pi sqrt(l/g) The Attempt at a Solution Well the thing is, I know I need to...

Having some trouble understanding derivatives including numbers to the "X" power. For example, f(x)= 7^8^x, f'(x)=? help please!

Natural Numbers - Pi, Log, ... Greetings, I'm far from an expert on math and I wanted to appeal to smarter minds to help compile a list of numbers with non-repeating chaotic decimals: Here's the first 2 (the only 2 I can think of) Pi e I'd also include the order of prime numbers...

Hi all, I'm a bit puzzled by one of my homework questions. I got an answer, but I have nothing to check it with and I'm not sure that my answer is correct. The question states that y=ln(ln(ln(x))), and asks for y'. This is what I've done, but it seems a bit too simple to me...

Hey, I really would appreciate some help with this one as I'm stuck on my coursework. It'll probably be easy for most of you but I forgot how to do this operation with logarithms. See this equation: lny = lnx + BlnK + (1 - B)lnL. How can I change that to one that removes the natural...

Somewhere a month or two ago, there was a discussion about E=mc^2 and the question of what the c^2 represents. The answer was that c^2 was simply a conversion unit, to put it in more common units of kg, m and s. That, if the formula were considered in more natural distance units of light...

Hi, I'm new here but have been working in the physics field for years. Most assume time to be infinite. But there appears to be a natural limit on the expansion of time. In the beginning, there was nothing and no possibility of change. How long this state lasted is a misleading question for...

Greetings mega-brains! :biggrin: A delta wing configuration, because it does not have a separation between the main wing and the horizontal tail which holds the pitch control surface(s), has a natural aerodynamic, temporary control reversal when initiating a pitch maneuver from a...

Can the concept of freewill ever be compatible with a natural philosophy?

hey 2day i had a test in intro calc and was given the following problem to solve: 50e^(2x) = 100e^(0.5x) i was quite annoyed :mad: at this problem because i didn’t know how to solve it. although i do know that natural logs need to be taken on both sides to solve it, however the...

Is there a way to find the,"Sum of the square roots of the first n natural numbers"?

All solids have a natural frequency but how do you determine its value? How would you determine it for a large building? I'll guess that for each different material they apply a constant external force with a specific angular frequency. The force with an angular frequency that breaks the...

If A is an n by n matrix of constants from the commutative ring k, and I is the identity n by n matrix, then Lagrange's expansion formula for determinants implies that adj[XI-A].[XI-A] = f(X).I where f(X) is the characteristic polynomial of A, and adj denotes the classical adjoint whose...

MTS buses "powered by clean natural gas" I saw several mts buses with signs "powered by clean natural gas". Are these buses really are powered by clean natural gas? If so, what is this natural gas? And why arent most forms of transportation uses this insteading the the polluting gasoline?

I am very interested in the economic production of natural gas from sub-sea methane hydrate formations. This development could have a huge impact on the worlds energy supply, as it has been estimated that 80,000 times more hydrocarbon is stored in hydrate formations than all other proven...

1) Write 2^2 * 3 * 5 as a natural number? I get 60 is it right or should i put 4*3*5= 60 2) Write 420 as the product of its prime factors in exponent form? What do i have to do ?

just wanted to know how i would differentiate y = ln(x^2 - 1)^3x i thought id first bring the 3x out in front and then do product rule but i don't think that yielded the right answer (i don't know the right answer btw but it didnt look right) y' = 3 ln(x^2-1) + 6x^2/(x^2-1)

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.

Can anyone offer a suggested article or website to understand Lee Smolin's idea of Cosmic Natural Selection (CNS)? Which of his books (if any) fully describes this concept? (Perhaps "The Life of the Cosmos") Since Smolin first came up with this idea, has he refined it in regards to the...

i have a few question, that i hope they will answered. 1) let w={0,1...,n,..}={0}UN, and let f:wxw->w such that the next requirements apply: a) f(0,n)=n+1 b) f(m+1,0)=f(m,1) c) f(m+1,n+1)=f(m,f(m+1,n). i need to prove that for every n,m in w, the next statement applies: f(m,n)<f(m,n+1)...

Can anyone please help me slove this example circuit i found. im having a hard time finding the initial current through the inductor and duno how to deal with the dependent source and inductor after the switch is opened.

At a time when there was a hose pipe ban, a person down the village noticed water gushing up from her lawn, she called severn trent (the local water authority and they told her ( it is not our problem it is a natural spring) for 5 weeks this lady watched her lawn being washed down the drain...

Oh my. Just a health FYI. http://health.discovery.com/centers/sex/libido/goat.html

will the natural resources ever end from Earth completely

I am doing a nuclear physics project for school and i can't find any diagrams which show exactly into which particles (gamma's beta's and alpha's) with how many electron volts U235 naturally decays and exactly how. Where do i find this kind of detail?

Find the first derivitive. Simplify if possible (factor). \begin{array}{l} y = x^{e^x } \\ \\ \ln y = \ln x^{e^x } \\ \\ \ln y = e^x \ln x \\ \end{array} There's a similar problem in my class notes where it was solved by taking the natural log of both sides. Is this...

This was one of the problems I encountered when I was in grade 6th. It was quite interesting I think. So I'm posting it here so that you guys can give it a try. ---------------- There exists or not exists a natural number that is just made up by the digit 0, and 1, and that number is divisible...

Interesting perspective on mathematics from a Nobel physicist. http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html Didn't know where to put something that is more or less math trivia. :smile: THE ROLE OF MATHEMATICS IN PHYSICAL THEORIES