Comparison Definition and 378 Threads

Homework Statement In the graph attached, why is isothermal graph line higher than adiabatic one?? Homework Equations The Attempt at a Solution At first, i had thought that work done in an isothermal process is greater than in an adiabatic process...but for comparison we would...

Series Comparison Test, URGENT help? Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for...

Hi, I've been working on this question which asks to show that {{P}_{n}}(x)=\frac{1}{{{2}^{n}}n!}\frac{{{d}^{n}}}{d{{x}^{n}}}{{\left( {{x}^{2}}-1 \right)}^{n}} So first taking the n derivatives of the binomial expansions of (x2-1)n...

Homework Statement use the comparison theorem to show that the integral of e^(-x^2) from 0 to infinity is convergent.Homework Equations None The Attempt at a Solution In class we have never dealt with using the comparison theorem with the exponential function so I was not sure what I function...

I'm given the following: 3/(n(2^(n-1))) I have to determine convergence using the limit comparison test. I've proved its convergent using the ratio test but am struggling with which term do I divide the above for the limit comparison test. Help?

How much stronger is the strong nuclear force compared it to the electromagnetic force beyond what could be accounted for by the inverse of the distance squared?

Homework Statement \sum^{∞}_{1}1/n^{n} Homework Equations Direct comparison test The Attempt at a Solution Since the main factor in the equation is the exponent that would be changing as n goes to infinity, I know that from the p series as p > 1 the the series converges. So I know...

Just as talked about in stewart in strategy for integration. I found notes online that also say: g(x) >= f(x) >= 0, then you want to prove convergence on g. If f(x) >= g(x) >= 0, then you want to prove divergence on g. I am pretty sure I follow the logic here, but how exactly does one pick...

Homework Statement For the sum from n=1 to ∞ (1/(sqrt(n^2+1)), I know you can use the limit comparison test to show that it is divergent but I was wondering if it is possible to compare this with 1/(2n)? I am not sure if 1/(2n) is always less than (1/(sqrt(n^2+1)) within those bounds. How...

Homework Statement Use the Comparison Theorem to determine whether the integral is convergent or divergent. \int_{0}^{1}\frac{e^{-x}}{\sqrt{x}} Homework Equations The Attempt at a Solution \int_{0}^{1}\frac{e^{-x}}{\sqrt{x}} \leq \int_{0}^{1}\frac{1}{x^{\frac{1}{2}}} Because p<1, the...

Homework Statement In cases A and B shown there are two positive charges +Q each a distance s away from a third positive point charge +q. Is the net electric force on the +q charge in case A greater than, less than, or equal to the net electric force on the +q charge in case B? Explain...

Homework Statement The original question is posted on my online-assignment. It asks the following: Determine whether the following series converges or diverges: \sum^{\infty}_{n=1}\frac{3^{n}}{3+7^{n}} There are 3 entry fields for this question. One right next to the series above...

Homework Statement The question says use the comparison to determine if ##\int_{0}^{1}\frac{e^{-x}}{\sqrt{x}}dx## converges. What should I compare to? Homework EquationsThe Attempt at a Solution

Homework Statement Two sites are being considered for wind power generation. In the first site, the wind blows steadily at 7 m/s for 3000 hours per year, whereas the second site the wind blows at 10m/s for 2000 hours per year. Assuming wind velocity is negligible at other times for simplicity...

I'm not sure if this is the right place for this question, but it was on the comparison between different model's AIC/SBC values. I ran a linear regression and got an AIC/SBC of .743/.768. When I ran the same regression in log-linear form I ended up with an AIC/SBC of -7.559/-7.534. My...

The title says it all really. Thanks.

Homework Statement Compare and contrast a 2.2 eV photonn with a 2.2 eV electron in terms of energy(J), rest mass (Kg) speed (m/s) wavelength (m) and momentum kgm/s. Homework Equations For Photon P=E/C F=E/h V=fλ λ= h/P For Electron λ=h/mv m=E/C2 p=h/λ Ke=1/2mv2 The...

Homework Statement a) Test the following series for convergence using the comparison test : sin(1/n) Explain your conclusion. Homework Equations The Attempt at a Solution i must show f(x)<g(x) in order for it to converge other wise divergence. g(x) = 1/n sin(1/n) >...

This isn't a coursework problem. I'm on winter break. Homework Statement A common approximation used in physics is: (1+x)n ≈ 1+nx for small x This implies that lim(x→0) (1+x)n = lim(x→0) 1+nx which is a true statement. However, lim(x→0) (1+x)n = lim(x→0) [(1+x)1/x]xn = lim(x→0) exn This...

I have two histograms that I would like to compare quantitatively. The values of the first histogram have respective relative errors for each bin. The second histogram has no statistical uncertainty. I could compute probabilities for each bin that the exact values would fall into a given...

Let f:[0,1]→ℝ be an increasing function. Show that for all x in (0,1], \frac{1}{x}\int_{0}^{x}f (t) \,dt \le \int_{0}^{1}f (t) \,dt So by working backwards I got to trying to show that (1-x)\int_{0}^{1}f (t) \,dt \le \int_{x}^{1}f (t) \,dt . While I know both sides are equal at x=1, the...

Use a comparison test to determine whether the series \sum (n+1)/(n^{2}+n+1) diverges or converges. I started out by simplifying the series to 1/n+1 and then from there I compared it to 1/n, which converges. 1/n is greater than 1/n+1 so based on the comparison test, the original series...

Hi all, new here and was wondering if you could help me out. I'm basically giving the two Milky Way models, and what was a common mistake (note it's a written piece not workings out) and I'd like to know if you think it makes sense/I don't waffle too much. Thanks in advanceThe attempt at a...

Homework Statement The question in the book is: "Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error. My problem is estimating the error I'm looking for. I just need help with finding the integral. Homework Equations ((sin n)^2)/(n^3) The...

Homework Statement Does the following interval diverge? \int^9_1 \frac{-4}{\sqrt[3]{x-9}} Homework Equations The Attempt at a Solution Well.. I've used the following function that I think is always less than the above function to prove that the function above DOES NOT diverge (by...

Homework Statement Determine whether the series converges or diverges. What I would like is some type of information on how to continue the problem. Homework Equations ∞ Ʃ √(n+1)/2n^2+n+1 n=1 The Attempt at a Solution I was thinking of doing a comparison test by doing...

\sum_{n=1}^\infty \frac{1}{n!} I understand what n! means, but I have no clue what to compare this to. It is obvious to me that the sum converges, but I'm not sure how to prove it. I assume I would compare it to a p-series but I need help. Thanks!

what is the basic difference between mutual exclusiveness and independence? actually i got this as a difference between fundamental principle of addition and fundamental principle of multiplication. it is quite urgent.

Alright here is my story: I took high school physics and loved it, went to college and took a class that is basically an algebra based physics class and a very light introductory just because I couldn't wait to get my hands on physics. When I was able to take Calculus based physics I did-- but...

I'm trying to understand relativity on a simple example: 2 objects A & B moving in exactly opposite directions at 0.6c each, starting from frame C at the center of things that remains stationary. So, we have: W <----0.6c A ...... C ..... B 0.6c----> E 1. From frame C, A is moving...

Homework Statement \sum_{n=2}^{\infty}\frac{1}{n\sqrt{n^2-1}} Homework Equations direct comparison test limit comparison test The Attempt at a Solution so i kind of cheated and looked at the back of my book and it says to compare with \frac{1}{n^{3/2}} so i tried using the direct...

Hello, I have a slight problem with Quantumtheory here. Homework Statement I have solved the schrödinger equation in the momentum space for a delta potential and also transferred it into real space. So now I have to find the correlation between the width of the wavefunction in both spaces...

Homework Statement Assuming planar orbits, calculate the Hohmann ∆V required to transfer from a low-Earth circular orbit with radius of 1.03 Earth radii to the orbit of the Moon (assume 60 Earth radii). Compare this to the 3-maneuver strategy of (1) escaping to infinity on a parabolic orbit...

integral 1/(1+x^2)dx from 0 to infinity I decided to compare that to 1/(1+x) (saying 1/(1+x) > (1/(1+x^2)) but this diverges when the original equation converges. Can someone explain why the integral 1/(1+x) was not a proper choice and what the process would be to find a correct comparison.

\int_{0}^{\frac{pi}{2}} \frac{cos(x)}{x^{1/2}} dx \int_{0}^{\frac{pi}{2}} \frac{cos(x)}{x^{1/2}} dx \le \int_{0}^{\frac{pi}{2}} \frac{1}{x^{1/2}} dx This would mean that the original equation was convergent. Was my reasoning correct in making the numerator 1 since the max value of cos(x) is...

what is the difference between router's ip address and my lan ip adress... what i understood is that we have a lan ip adress and a wan ip adrress ...now my wan ip address is found using what's my ip address address.com and it changes...hence dynamic...and my lan ip address is using...

Homework Statement Prove or disprove: b\int_b^∞ f(x) dx ≤ \int_b^∞ xf(x) dx for any b≥0 and f(x)≥0Homework Equations N/A The Attempt at a Solution Ok this question has caused me quite some problems. I have come to the conclusion that this needs to be proven rather than disproven...

2 problems, I need to use the direct comparison test with either a p series or a geometric series 1)series of j^2/(j^3 +4j +3) I thought of comparing it to j^2/J^3 which comes out to 1/j, but that dosent work, my teachers answer is you compare it to 1/5j 2) series of sqrt(q)/(q+2) I would...

Hi all, I am trying to devise a mathematical model for my project I am working at. Description is as follows: we have a sample space \Omega=\{w_1,w_2,\cdots, w_N\} It is very large. Suppose further, that we have some assumption of frequency of occurrence of each w_i , stored in...

Homework Statement Determine the Convergence or Divergence of \sum_{n=1}^\infty\left(sin(1/n)\right) Homework Equations limit comparison test The Attempt at a Solution I don't know what to compare this series to, I tried the harmonic series to get sin(1/n)/(1/n) = nsin(1/n) which...

Homework Statement Does the following series converge or diverge (use either the Limit Comparison or the Direct Comparison Test): \sum_{n=1}^{+\infty} \frac{3^{n-1}+1}{3^{n}} Homework Equations In a previous problem that was \sum_{n=1}^{+\infty} \frac{1}{3^{n-1}+1} I was able to...

In the essay „Über die Ablenkung des Lichtes I am Schwere*feld der Sonne“ ( http://adsabs.harvard.edu/full/1931ZA...3..171F ) the authors - Freundlich, Klüber and Brunn - presented 1931 graphically the results of three expeditions, which took place 1919, 1922 and 1929. They put together all...

Homework Statement \int \frac{arctan(x)}{2+e^x}dx where the interval of the integrand is from 0 to infinity. In order to use the comparison method I need to compare 2 functions but I am having so much difficulty figuring out what function to compare it to. Its not just this particular...

Homework Statement (a) By using a suitable transformation, show that the normal form of the DE y'' - 2y' + (x+1)y = 0\;\;\;\;\;(*) is Airy's equation u'' + xu = 0. (b) State the Sturm comparison theorem for zeros of 2 second order linear DEs in normal form. (c) By comparing with the DE...

Homework Statement Summation from n=1 to infinity: (e^(1/n)) / n Homework Equations The Attempt at a Solution Can someone point out what criteria I should be considering when trying to determine which test to use? I was looking at a comparison test as a way to go on this one...

Problem: Summation from n=1 to infinity: 1/(n^3 + n^2) I understand, for example, another problem wherein it is 3/(4^n + 5) what you would compare that one to but how do you go about breaking this one up with two "n" terms? Are you supposed to, in general, pick the largest value of n? So...

Im practicing problems for my Calc 2 test tomorrow. I am doing this problem which I am not quite sure I've done it right. I think I have, but I want confirmation... \sum_{n=1}^{\infty} \frac{1}{\sqrt(n+4)} I chose my comparison series as \frac{1}{\sqrt(n)} and then ran a limit test...

Homework Statement If i have the series ln(k)/k^2 would I compare it to 1/k^2? The reason why I'm confused is that ln(k)/k^2 > 1/k^2 so if its greater than a function that converges it doesn't tell us anything right? So I'm not sure what exactly to compare it with on account of the ln(k) in...

Homework Statement Before I state my problem, I need to quote this from my book http://img18.imageshack.us/img18/3748/comparisonnr.th.jpg Uploaded with ImageShack.us http://img806.imageshack.us/img806/8665/integraltest.th.jpg Uploaded with ImageShack.us See the problem here...

Homework Statement Use the Comparison Theorem to evaluate whether Integral(dx/(x*sinx)) on 0->pi/2 converges or diverges. The Attempt at a Solution I don't understand what to do about 0. Am I allowed to compare it to 1/x even though 1/x is undefined at 0? Like-wise am I allowed to...