Natural Definition and 1000 Threads

Homework Statement Prove by induction that \binom{n}{k} is always a natural number. Homework Equations The problem requires that we use the fact that \binom{n+1}{k}=\binom{n}{k-1}+\binom{n}{k}\tag{1} The Attempt at a Solution Well, the first part of this question requires a...

Homework Statement lnx+ ln(x-1) = 1 solve each equation for x Homework Equations ln(e^x) = x e^lnx = x The Attempt at a Solution x + (x-1) = e^1 [==> using ln(e^x) = x] from this point on, I am stuck because I am having trouble isolating x because of the x that is in the brackets...

Homework Statement Guys how come ln(e)=1 ? How can l prove this

Please look into this site http://knol.google.com/k/alex-belov/paradox-of-classical-mechanics-2/1xmqm1l0s4ys/9# The experiment 2 animations This is animation based on classical mechnics laws http://mysite.verizon.net/vze27vxm/sim.gif This is animation based on theory of...

Homework Statement Show that the natural logarithm is not subadditive. You could use ln(1/2+1/3)\leqln(1/2)+ln(1/3), but mathematicians view all such numerical evidence as an invalid proof. Homework Equations ln(a+b)\leqln(a)+ln(b)The Attempt at a Solution ln(1/2+1/2)\leqln(1/2)+ln(1/2) Well...

Homework Statement 10(1 + e-x)-1=3 Homework Equations The Attempt at a Solution I'm supposed to solve for x, but I don't know how to go about this. I tried dividing the 3 by the 10, but after that I don't know what to do. I believe I should use ln on both side, but that's after...

Homework Statement I need to use MATLAB to solve these problems. http://users.bigpond.net.au/exidez/IVDP.jpg Homework Equations MATLAB The Attempt at a Solution a) R1=3.6; R2=R1; C1=33*10^-6; C2=22*10^-6; % defining the polynomial constants Vs=[R1*R2*C1*C2...

Homework Statement Find all the natural domain of the function algebraically, and confirm that your result is consistent with the graph produced by your graphing utility. h(x) = 3/2-cosx Homework Equations (a) h(x) = 3/2-cosx (b)x2-1/(x+1) The Attempt at a Solution Do I need to...

ok. some rant about definition and semantics. integers are isomorphic ordered pairs of natural numbers (a,b) w/ equivalence relation (a,b)=(c,d) iff a+d=b+c. reals are convergent sequences of rationals, etc. in mathematics, are integers simply isomorphic to the ordered pairs of...

In class we defined convergence as \forall\varepsilon>0\;\;\;\exists\mathrm{N}\epsilon\mathbf{N}\;\;\;\forall\mathrm{n}\geq\mathrm{N}\;\;\;\left|a_{n} \right|<\varepsilon So if a sequence {a_n} of real numbers converge to 0 if for every ε > 0 there is N s.t. |x_n| < ε for n ≥ N... Is the...

Hello, Can we interchange the natural logarithm "ln" operator and the integral operator? Regards

Homework Statement Find the sum of the series, if it converges, of n=1 to infinity of ln(n/(n+1)) The Attempt at a Solution My intuition tells me the series converges because as n goes to infinity the series is taking the log of 1, which is 0. How to sum it though... I have no...

than other skills? At least, that's the general impression I've seen people keep. If you see the best basketball player, it's just hard work and dedication, and people tend to think you could become one of them if you put enough effort and dedication. But if you hear someone singing...

What kind of operation exists that is valid for a group limited to the natural numbers?

Homework Statement Prove that every Natural number is either even or odd. Homework Equations Mathematical Induction Even: n = 2k where k is an integer Odd: n = 2k + 1 where k is an integer The Attempt at a Solution I think I have a relatively complete proof, however, it doesn't...

It might be a silly question but I was just wondering if this was unprovable or false... Thanks guys

Hi How do you calculate the natural frequency and vibrational response of a space frame and what is its damping characteristic? What are all the aspects to take into considerations and how do you analyse failure due to vibration? Thanx

What does the natural frequency of an object depend on? Whenever I try to look this up, I usually read that the natural frequency depends on "intrinsic" properties or a "variety" of factors. Is the natural frequency independent for each object/is there any universal factor the natural...

Hello I was talking with someone bout natural vs supernatural when it relates to something such as ID and one thing that seems to be a hurdle is , are they mutually exclusive or not? Is there a book or website that does a good job discussing it?

I know that there is a year old thread that has just been resurrected that is slightly on this topic, but I had a question that I thought might merit a new thread. I'm working with my Calculus book here, and I'm working on the chapter called, "Logarithmic Functions from the Integral Point of...

I have a transformer in a box that is cooled using natural convection. There are louvered openings on the box to pull cool air in the bottom and let heated air out of the top. How do I determine how much heat is actually leaving the enclosure? Info that I have is the area of the enclosure, the...

im confused as to what the integrals and differentials of log and ln are. i looked up the derivative of log x and it said it was 1/x so then the integral of 1/x should be log x but i thought it was ln x im so confused! please help me just say integral of log x differential of log x...

By using the term "common ethics" I am referring somewhat to the idea of "common sense". You see it everyday in traffic, among pedestrians, in classrooms and everywhere there is human activity. We could say you can find it in the animal and plant kingdoms as well, but that would be an outright...

hello, I was trying to figure out what will be the y value for this equations: 1 - e^-0.15*10^-5*y = 0.1 Could somebody help me in this?? The answer is supposed to be 70,240. thanks.

Hi Natural frequency of spring is fn = 1/(2*pi) * sqrt(k/m), where k = spring constant and m is the mass. Ok, so I have a spiral spring which means that spring is coiled couple of times. Its spring constant is (according to Hartog's Mech. Vibrations), k = E*I/l, E=Elastic Modulus, I = Inertia...

Homework Statement A Consistency question regarding the dimensions of the KG Equation. Homework Equations M^2=\frac{\hbar c}{G} for a quantization of gravitational charge on matter The Attempt at a Solution I know a few things however concerning the KG equation. It is directly...

Homework Statement If 6 J of work is needed to stretch a spring from 10 cm to 12 cm, and another 10 J is needed to stretch it from 10 to 12 cm, what is the natural length of the spring? Homework Equations W=FD Hooke's Law The Attempt at a Solution Honestly, I stare at this problem...

HI when dealing with natural convection, we use grashof's number. suppose we have a heated plate of temperature Tp. and heat being transferred to surrounding air by convection, air of temp Ta. So film temp is Tf = 0.5(Tp + Ta) If grashofs numbers, Gr = \frac { \beta gL^3 \delta...

Homework Statement Show that for any natural number K, there is an n large enough so that (2^n) > K. Homework Equations The Attempt at a Solution K is a natural number -> the smallest possible K would be 0 (lower bound?) and the smallest 2^n is 1 when n = 0, and the upper bound...

Hi guys, I need to find the natural frequencies of a series of pressure rakes. We have a numerical model, but I'd like to confirm with a hand calculation. I would like to model the pressure rakes as a cantilevered beam with varying cross section (i.e. as each tube "stops" the beam decreases in...

Hey all, I'm really having a hard time figuring out a couple of problems in which I have to differentiate: 1: \frac{e^3^x}{\ln x} I just don't know how to put it together... I know that e^3^x is 3e^3^x, and I know that you can't different \ln x, so I don't know what to do from there...

Title says all.

Can someone please tell me how to expand \ln(x + \sqrt{1+x^2}) for small x? I'd like to retain terms at least up to order x^5. Thanks!

Homework Statement Hi all, I'm having an issue with a homework problem. I'm taking a vibrations class and in our lab we had a cantilever beam with a mass on the end. There is an accelerometer on the beam and we used an impulse hammer to hit the beam. We had software that recorded all the...

I have to prove that for all k,m,n \in N that if m+k = n+k, then m=n. The problem mentions that I must prove this by induction. I did the base case k = 0: If m+0 = n+0, by identity m=n. Then I attempt to show that m+1 = n+1 implies m=n, but I am stuck, I don't see how induction can be...

ln(x+1) + ln(x+3) < ln(x+7) Find x! I should of course know this, second year at high school (in Norway). I've just forgotten the way attack the whole thing^^

Homework Statement \displaystyle\int\left(\dfrac{\ln x}{x}\right)^2 dx 2. The attempt at a solution I tried letting u=\ln^2 x and dv the rest and I also tried dv=\ln^2 x dx and u the rest. It won't work out.

This is perhaps a stupid question but: When we use natural units and set h=c=1, do we choose appropriate units so that their value is one but these constants still have dimensions, or are we somehow choosing h=c=1 to be a pure number with no dimensions?

Homework Statement Let a,b \inR with a < b. and let n \inN where n(b-a) > 1. a) How do you know that such an n must exist? b) Show that there exists m \inZ where a < m/n < b c) Show that there exists some irrational c where a < c < b (Hint:rational + irrational = irrational.) Homework...

I'm certain this is a silly question but: Do photosynthetic plants require natural sunlight to undergo photosynthesis, or will artificial light from flourescent lights suffice? Thanks!

Homework Statement Hi. I want to solve: \frac{d\ln(-x)}{dx}. When using the chain rule I get: \frac{d \ln(-x)}{dx} = \frac{d\ln(-x)}{d(-x)}\frac{d(-x)}{dx} = -\frac{d\ln(-x)}{d(-x)}. But how do I find the last derivative? I know by experience that it is -x-1, but how is the derivation...

Hi, I'm a 2nd semester student in the Indian Institute of Technology, Kanpur. My fields of interest are AI, particularly machine learning, pattern recognition etc. I have done a project on pattern recognition in the Indian Statistical Institute, Kolkata. I've some ideas about constructing...

Dear PF members, In terms of natural units the reduced Planck's constant (\hbar) is 1 ML2T-1. Now in this terminology how a magnetic field can be expressed? thanks for your reply, rajini

If n is a natural number then n2+n+3 is odd. This is what I have and wanted to know if I was doing it right or not: Let n be a member of the natural numbers. If n is even, then n=2k, k member of natural numbers, and n2+n+3 =(2k)2+2k+3 =4k2+2k+3...

Homework Statement How would I begin to integrate ln(t+1) from 0 to e^2x? Homework Equations d/dx[log base a of u]=1/(lna)u du/dx Can the original equation be manipulated to use this derivative? The Attempt at a Solution Not sure where to start.

Pardon me for my ignorance -- and naivety, if this question idicates it -- but would it be possible to change the rotation of a planet or moon? We'll assume the hypothetical people attempting this project have a nearly infinite budget, but even with quadrillions of dollars, is this even...

Homework Statement Find the inverse equation (i.e. solve for x) y=(e^x)/(1+2e^x)2. The attempt at a solution e^x = y(1+2e^x) x = ln(y) + ln(1+2e^x) ? Profit! I can't figure out what to do with ln(1+2e^x) to get the x out of there so I can finish isolating x. I tried balancing it another way...

Hi, how would you show that 4^(k)+4 * 9^(k) \equiv 0 (mod 5)

The text I'm reading explains how there is a natural isomorphism between a vector space and the dual of the dual of the vector space. The author explains that this is so because the isomorphism he defines makes no reference to a specific basis of the vector space. I understand that natural...

Why do some people define the natural numbers as the integers 0,1,2,3... while others define them as the integers 1,2,3... ?