Natural Definition and 1000 Threads

Hello, I am fairly new here, so thank you in advance for your help. This is not a homework problem, just one of curiosity based on my limited knowledge of asymptotic expansions. I'm curious about how the function ln(x) or ln(1+x) behaves for large values of x. Plotting in Matlab, I see a linear...

Hello people. I'm a freshman in college and I'm looking forward to enter an advanced mathematics program. The admission test is basically number theory & sometimes I get stuck with some questions (I'm using Spivak's Calculus to study). I'm stuck on question 8, chapter 2. "Prove that every...

Does anyone know of a device that will measure the percentage of CO2 (about 5% and resolution down to 0.1%) in natural gas, in real time, the gas is at approx 40 bar and 30 Deg C. Thank you

Earlier today, I was thinking about the statement that "there exists no greatest natural number" and immediately, two proofs sprang to my mind. Since my question depends on these, I'll write them out below . . . Proof 1: Let n \in \mathbb{N}. Clearly n+1 \in \mathbb{N} and n < n+1. Since...

Homework Statement f(x,y,z)=exy and x5+y5=64 Find Max and MinHomework Equations ∇F = <yexy, xexy> λ∇G = <5x4λ, 5y4λ> The Attempt at a Solution yexy = 5x4λ xexy = 5y4λ x5+y5=64 No idea where to go from here...

Homework Statement Trying to solve for K: ln(1-4k)=-6k Homework Equations The Attempt at a Solution I know that need to take the e of both side, to get 1-4k=e^-6k, but I cannot remember any properties of e to allow me to remove the k from the exponent. Any tips is appreciated.

Homework Statement 3. (a) Let f(x) = ln(x^2-1), and [itex]g(x)=\frac{x}{\sqrt{2-x}}[/tex] (i) Find the natural domains of f, g, f + g, \frac{f}{g}, and \frac{g}{f} Homework Equations N/A The Attempt at a Solution I know that the natural domain of f(x) is x belongs to real...

I wanted to know what is the minimum critical mass of natural uranium (99.28% U-238) when moderated by beryllium and light water, when in a optimumally designed lattice. As can be seen in this article (google Plutonium Production Using Natural Uranium) criticality is attained at about 10 tons of...

Homework Statement A thin beam of length L (flexural Stufness EI, cross-sectional area A, density p) is connected to a linear spring of stiffness K_s at each end. Derive the governing equation for the natural frequencies of transverse vibrations from the beam equation and boundary conditions...

Homework Statement I keep getting what I think is the "right answer", but it's not one of my choices :^( Here are the problems and answer choices. 1). 2). Homework Equations nothing really...or at least I don't think besides the fact that e^-x = 1/e^x The Attempt at a Solution 1). x + 14...

Homework Statement I am new at logic and I'm stuck on a problem set: a) (~C \vee (A \cap B)) \vdash ((~C \vee A)\cap (~C \vee B)) b) \vdash ((A\cap B) \leftrightarrow (B^A)) c) \vdash (((A \rightarrow B) \rightarrow C) \rightarrow (A \rightarrow (B \rightarrow C))) d) ((A...

Homework Statement \int^{4}_{2} \frac{dx}{x\left(lnx\right)^{2}} Homework Equations Let u=lnx du=\frac{1}{x}dx x=2 \rightarrow u=ln2 x=4 \rightarrow u=ln4 The Attempt at a Solution so with the u substitution we have: \int^{ln4}_{ln2} \frac{1}{u^{2}}du which goes to...

Homework Statement This is actually only related to a problem given to me but I still would like to know the answer. From my understanding, Cantor's Diagonalization works on the set of real numbers, (0,1), because each number in the set can be represented as a decimal expansion with an...

Homework Statement A thin, flexible metal rod has a length of 0.606 meters. One end of the rod is clamped to a table, and the other end can vibrate freely. What are the first three natural frequencies of the rod if the wave speed in the rod is 27.4 meters per second? Hint: Draw pictures of...

Homework Statement The speed of transverse waves along a stretched spring is 9.05 meters per second. The spring is 4.70 meters long and is held in place at both ends. What are the first three natural frequencies of the spring? Hint: Draw pictures of what the spring will look like when it is...

Claim: every natural number n can be uniquely expressed in the form n = 2jo + 2j1 + 2j2 +...+ 2jm where m≥0 and 0≤jo<j1<j2<...<jm. =========================== So I think we need to prove two things: (i) existence and (ii) uniqueness. My idea is to prove existence first by mathematical...

what is the convention you adhere to when it comes to natural numbers? for example there is a long standing debate about 0... should we define \mathbb N = \{0,1,2,...\} or instead \mathbb N = \{1,2,3,...\} and more about this, considering Peano's Axioms than we could choose \mathbb N...

Hello physicsforums members, I am an engineering student at Purdue University and am currently conducting research with regards to ribbon transducers. A ribbon transducer consists of a rectangular element of metal foil suspended within a magnetic gap (ie free at the sides) and...

I was pondering square numbers today, and I noticed something interesting: every natural number contains information to construct a Pythagorean triple. Let me show what I mean for an odd natural number, also using the binomial theorem for square quadratic equations (equations of the form...

Homework Statement Solve ln(sinh-1(x)) = 1 (Just give the formula for x, no calculator is necessary) sinh-1(x) = asinh Homework Equations The Attempt at a Solution When I did this, I knew sinh-1(x) = ln(x + sqrt.(x^2 +1), but the equation would look like ln(ln(x +...

Homework Statement This is my first time ever posting anything on here...but we just started working with ln? I know that it's the base e? or something like that... but the problem is this... 1/3=ln(x^2/x-4)Homework Equations The Attempt at a Solution I haven't attempted..i...

Homework Statement I'm trying to figure out the the boundary of the set of all 1/n, where n is a natural number. Consider this as a subset of R with its usual metric, nothing fancy. Homework Equations There are at least two "equivalent" definitions of the boundary of a set: 1. the boundary of...

I have the following function: y= (sqrt(8x^4-5)) / (x-1) take the natural log of both sides: 1) ln y= ln (sqrt( 8x^4-5) - ln (x-1) OR 2) ln y= 1/2 ln(8x^4-5) - ln (x-1) Which one is correct? I know when i take the natural log of a/b its ln(a)- ln(b)... but also when i take...

Hello, I made a mistake in the title of this thread and this question is on general logarithms; loga(aloga(x)) = loga(x) ==> aloga(x) = x Can someone enlighten me on why loga(aloga(x)) simplifies to loga(x)? Can someone prove why this is true? Futhermore, why does this imply that...

This equation specifies displacement x in terms of motion time t (starting from rest). x = \tau g\left(t + \tau e^{-t/\tau} -\tau\right) where tau = m/b is the system time constant of a mass m suspended from a mechanical braking device with rectilinear damping constant b and g is standard...

Homework Statement True or false? ln(1/10) = -\int dx/x The Attempt at a Solution I have no idea where to start on this one. what is dx/x ??

Homework Statement Ok, this is not homework, just something that's been bugging me and my tutor is unavailable(as usual) to help me. Why does increasing the mass of a system lower its natural frequency, like adding a concrete block to a washing machine. Come to think of it, I'm not even too...

fin all natural numbers n that n\sigma (n) \equiv 2(mod\varphi(n))

How does (ln(x))^(1/x)=ln(x^(1/x))? A friend told me this was a true statement but could'nt prove it. If that isn't true, then how would you find the lim x->0 of (ln(x))^(1/x) using L'Hospital's Rule?

Shortly after the year 2001, to now, there have been more increasingly violent earthquakes, hurricanes, tsunamis, tornadoes, etc... than in any other decade in history. I wanted to know if there is a natural, geological, and meteorological explanation for this. Not too long ago, there were Two...

1. Consider an oscillating system of mass m and natural angular frequency omega_n. When the system is subjected to a periodic external (driving) force, whose maximum value is F_max and angular frequency is omega_d, the amplitude of the driven oscillations is A=\frac{F_{\rm...

Hi All, Been try at this for a week now and I know I'm missing something. I'm too far out of university to remember how to do it, but just close enough to know that I should remember. Anyway, I have a steel can containing a mixture of liquidfied hydrocarbon gasses...

Is atheism incompatable with the concept of natural rights? Most (or at least some) adherents to natural rights argue that human rights come from a god, or that there is an absolute morality that is the basis of natural rights. Atheists obviously do not believe in a god and most would...

1. Graphing Carefully: Sketch f(x)= 10(ln(ln(x))/ln(x) accurately using calculus, your calculator, or both to aid you. Make sure to include all vertical asymptotes, as well as local extrema 2. f(x)= 10(ln(ln(x))/ln(x) 3. OK. I might come across as stupid but here goes... I don't...

Homework Statement lim(e-2x cosx) x-> infinity The Attempt at a Solution I thought right away that the limit would not exist because of cos x oscillating the function between + and - but the answer in the book says zero. I need help figuring out why my thinking was incorrect.

Homework Statement lim e3/(2-x) x->2+ The Attempt at a Solution I can't seem to get started on this one.

Hello! Question: if it is asked to prove a statement A(n_1,...,n_k) for all natural numbers n_1,...,n_k, is it actually enough to check its truth by induction on just one of the counters, say n_1?

I have a theoretical question. Does a structure's natural frequency have anything to do with the highest frequency of which it can vibrate? Or can the structure vibrate in any multiple of the natural frequency (until it brakes...)?

I have just started to study resonance and I don't quite understand what it is. My textbook says: "All objects vibrate with a characteristic "natural frequency". When an object is forced to vibrate at its natural frequency, the amplitude of its vibration can grow very large. This effect is...

Homework Statement Prove that \binom{n}{k} is a natural number by showing that \binom{n}{k} is the number of sets of exactly k integers each chosen from 1, ..., n. Homework Equations The Attempt at a Solution I posted a similar question before...

Can someone explain to me how they get last line to work out? I am confused on how they're using natural log with limit problems. Thanks for the help! :)

Homework Statement (ln(1+e^x))^6 Homework Equations The Attempt at a Solution Honestly I haven't done this in 3 years and a friend asked me to help them with it. I'm at a bit of loss.

Q1) If (x^5)-x = 8 then x = e^(solve for this) not sure, x*x*x*x*x-x = 8 help please - q2) ln(3x)/x^2 dy/dx = [ ]-[ ]ln(3x) / x^3 or solve for dy/dx I get (x^2)*(dy/dx(ln(3x))) - ln(3x)*(dy/dx(x^2)) / x^2*x^2 =(x^2)*(1/x) - ln(3x)*2x / x^4 =...

Homework Statement y and x are both close to 1. ln(y) - ln(x) \approx (y-x)(lnx)' Can someone explain me why this is true? By the way, (lnx)' is the derivative of lnx, which is just 1/x The Attempt at a Solution I guess this is something to do with the taylor series of ln(x). I tried to...

Preparing for the math test, and cannot understand what to do for one of my practice problems: I need to find if the series is convergent or divergent, using test for divergence (divergent if limit doesn't equal 0) sigma from 1 to infinity of ln((n^2+1)/(2n^2+1)) I see that I should use...

When a forced oscillation is damped, it is true that the frequency at which resonance occurs decreases right? so does this mean that the natural frequency has decreased too or does it only mean that resonance does not occur at natural frequency when being damped?

Can anybody solve for x? 6=(36/9)ln(120/x) The answer is x=22.3 I have so far got: 6=4*ln(120)-ln(x) 6=19.15-ln(x) I think it may be incorrect

Could we set the natural value Hubble constant to be 1 in some calculation of cosmology, like what we do in the natural unit?

You might be interested in this paper: Jaramillo, P., W. M. Griffin, and H.S. Matthews. 2007. Comparative life-cycle air emissions of coal, domestic natural gas, LNG, and SNG for electricity generation. Environmental Science & Technology, Vol. 41, No. 17, 6290-6296 You can download it here...

Let us define the charge of the down-quark, up-quark, and electron as (-1/3, 2/3, -1)*3 or -1, 2, -3. Let momentum in some closed one dimensional space be equated with electric charge. If momentum goes as n/wavelength where n = 1,2,3,..., the down quark has a charge of -1, wavelength equal...