Comparison Definition and 393 Threads

would someone please care to reword this proof for me? http://en.wikipedia.org/wiki/Limit_comparison_test it talks about ε, which is not even defined and then n0, which is again not defined, what the hell are all these variables... I'm sure someone here could do a better job organizing...

I remember having great confusion when I first read about electromagnetic waves. I remember being introduced to a historical text about ether when I was a child, and thinking it was an unsolved puzzle. I'd never really been able to shake the question "What does an electromagnetic wave propagate...

Hi, I would like know if it is possible to tell which function is better over another? For instance, I have two functions: (i) f(x,y)=exp(a*x) * exp(b*y) (ii) f(x,y)=a(exp(x)) * b(exp(y)) I would like to know the characteristics of both the functions which make it better/less better over...

Learning about the Limit Comparison Test for Improper Integrals. I haven't gotten to any applications or actual problems yet. Just learning the theory so far, and have a question on the very beginning of it.Homework Statement f(x) ~ g(x) as x→a, then \frac{f(x)}{g(x)} = 1 (that is, f(x)...

Hello everyone, I need some help on doing convergence tests (comparisons I believe) on some Ʃ sums. I have three, they are: 1. Ʃ [ln(n)/n^2] from n=1 to ∞. I tried the integral test but was solved to be invalid (that is, cannot divide by infinity). Therefore I believe it to be a...

Homework Statement I must calculate the probability that the position of a harmonic oscillator in the fundamental state has a greater value that the amplitude of a classical harmonic oscillator of the same energy.Homework Equations ##\psi _0 (x)=\left ( \frac{m \omega}{\pi h } \right ) ^{1/4}...

I know we have the following \big | \int^{b}_{a} f(t) \, dt \big | \leq \int^{b}_{a} |f(t)|\, dt 1- How to prove the inequality ,what are the conditions ? 2- Does it work for improper integrals ?

Homework Statement Show that: \sum \frac{3}{n^{2} + 1} converges from n = 1 to ∞ Homework Equations If Ʃbn converges, and Ʃan < Ʃbn. Ʃan also converges. The Attempt at a Solution \sum \frac{1}{n^{2}} converges \sum \frac{3}{n^{2} + 1} = 3 * \sum \frac{1}{n^{2} + 1}...

Homework Statement I need to use the Comparison Test or the Limit Comparison Test to determine whether or not this series converges: ∑ sin(1/n^2) from 1 to ∞ Homework Equations Limit Comparison Test: Let {An} and {Bn} be positive sequences. Assume the following limit exists: L =...

If one planet has a higher gravity than another, would that mean that it would progress through time at a slower rate than the other, being 'deeper' in a gravity well? That it would 'age' slower, relatively?

Homework Statement Is the series convergent or divergent? \sum_{n=0}^{\infty}{\frac{1}{\sqrt{n+1}}} Homework Equations I can use any test but wolfram alpha says that it is divergent by comparison test. The Attempt at a Solution How do I apply comparison test? I can compare it to: \sum _{...

Homework Statement Why is it that when using the comparison theorem my limits of integration must be from a constant value to infinity and not from negative infinity to infinity? For example ∫ x/(1+x^2) dx from -∞ to ∞

I'm not really sure when each of these should be done. In fact, I don't really understand the reason that we use the limit comparison test. Σ1/(n^2+1) So here I can simply say that P=2>1, so the original converges. Σ1/N^3+N^2 Here, I would say that P=3>1, implying the original...

Homework Statement Use any test to determine whether the series converges.Homework Equations \displaystyle \sum^{∞}_{n=1} tan(1/n) The Attempt at a Solution Direct Comparison Test tan(1/n) > 1/n By integral test: 1/n diverges thus, by dct, tan(1/n) diverges.

Hi guys, Just doing a few calculations on a homeloan and comparison rate calculation has got me stumped. Loan Amount: $320,000 Loan Time: 30 years Interest Rate:5.55% Initial Costs:$4463 Monthly Fee: $15 So from this, with a fortnightly compounding frequency, I calculate the total...

Homework Statement evaluate the integral 1/(u^2 -36) from 0 to 6 does the integral converge? Homework Equations The Attempt at a Solution integral 1/(u^2 -36) integral 1/((u-6)(u+6)) Partial fraction decomposition 1/((u-6)(u+6)) = A/(u-6) + B/(u+6) 1=A(u+6) + B(u-6) 1=(A+B)u +(6A-6B) A+B=0...

Homework Statement use limit comparison test. Homework Equations \displaystyle\int_2^∞ {\frac{1}{\sqrt{x^2 - 1}} dx} The Attempt at a Solution I have tried usin 1/x as the comparison function, but when applying the test it comes out to 0, not an L -> 0 < L < ∞

Momentum and magnetic fields are both vector quantities. If two bodies with the precise mass and speed collide head on (θ = 0), then momentum is conserved (they come to a complete stop) and energy is conserved (the kinetic energy is changed to other forms). What then happens in the case of...

Homework Statement Use direct comparison test or limit comparison test to determine if the integral converges.Homework Equations \displaystyle\int_0^6 {\frac{dx}{9-x^2}} The Attempt at a Solution If i were to use the limit comparison test, would these integrals fit the criteria. ** if the...

Homework Statement Find all positive values of b for which the series Ʃ bln(n) converges. Bounds are from n=1 to infinity. Homework Equations The assignment is for Direct Comparison Test and Limit Comparison Test. The Attempt at a Solution I don't know where to begin. Using a comparison...

Hello all. I am now enrolled at VRI at WWU! I am working on a sort of independent study project. I am making a V12 out of a pair of motorcycle engines to go into a VW based kit car. I have run the IHP formula and come out with 250hp, and 220 lb/ft of torque. The car weighs 1800 pounds...

Homework Statement if we apply a force of 56 n on 40 degree angle above the horizontal than how would the results compare if it was applied 40 degree below the horizontal?Homework Equations none The Attempt at a Solution i said that it would be the same and different depending on how we look...

Homework Statement Q3. Sampling and reconstruction A) It is common practice to use low order low pass filters instead of a Sinc filter, at the expense of a higher sampling rate. Here we investigate how to do this. Compare: a) the ideal reconstruction of a low pass sampled signal, which can be...

I am looking for a paragraph on each metal on the comparison of aluminium and stainless steel under the heading: Manufacturing Methods: What processes are available to turn the raw material into products and how do the processing methods differ? Regards, Lockyphysics

Homework Statement A few examples done in class that I didn't understand are as follows: (Find out if convergent or divergent) integral 0-->infinity ( x / (x^3 + 1) ) integral 1-->infinity ( (2+e^(-x) ) / x ) Homework Equations None The Attempt at a Solution Basically, I have NO idea...

Homework Statement Using the limit comparison test to determine convergence or divergence (1) \sum^{\infty}_{n=1} \frac{(ln(n))^{3}}{n^{3}} (2) \sum^{\infty}_{n=1} \frac{1}{\sqrt{n} ln(x)} (3)\sum^{\infty}_{n=1} \frac{(ln(n))^{2}}{n^{\frac{3}{2}}} Homework Equations...

Homework Statement The Attempt at a Solution I currently think that a and e are correct. But I am not sure what happens to the energy IN THE BOX. When the box explodes, the energy of the contents changes from potential to thermal, sound and kinetic energy. Thus by conservation of...

Do glasses work in the same way that a magnifying glass does. They take light and focus it onto a point? If a magnifying glass can burn an ant, do eye glasses burn our eyes to a certain degree? Could it just be that eye glass wearers don't stare at the sun? I hope you guys understand what I...

Are you familiar with multiple languages? This is the thread to discuss what languages you like the best, what advantages/disadvantages they have over others, etc. I am familiar with C, Python, Ruby, Scratch, and JavaScript. That's all I can think of. IMHO: Python and Scratch definitely...

Is there some fundamental fact of the universe (Quantum Mechanics) that prevents us from removing noise (without having to compare the entangled particles)? In the quantum eraser experiments: To get ("un-embed") the interference pattern i.e. to separate the entangled particles from the...

Homework Statement Determine if the following integrals are convergent or divergent. Explain why. \int^{1}_{0} \frac{1}{1-x^{4}} dx The Attempt at a Solution I've tried using Comparison Test, using f(x) = \frac{1}{1-x^{4}} and\; g(x) = \frac{1}{1-x}, 0 \leq f(x)\leq g(x) in ] 0,1 [ and I...

Hi all, I have this question, and hope you could help me to solve. There are two engines with the same displacement (say 250cc). One with smaller piston and the other bigger. Of course the first one will move longer. If everything else is the same or similar, generally, which engine is...

Which one of the following weighs less when weighted in magnetic field? A>SnCl3 B>FeCl3 C>TiCl3 D>VCl3 This is the question I encountered in my Chemistry Olympiad. While I went with B, my institute published answer as A. What I deduced is that A is diamagnetic while the rest are...

The Problem: Let a(n) = (n^2)/(2^n) Prove that if n>=3, then: (a(n+1))/(a(n)) <= 8/9 By using this inequality for n = 3,4,5,..., prove that: a(n+3) <= ((8/9)^n)(a(3)) Using the comparison test and results concerning the convergence of the geometric series, show that: The...

Homework Statement Two identical samples of ideal gas are initially at P1 and V1. The first sample undergoes an isothermal transformation to P2, V2 and second sample undergoes an adiabatic transformation to P3, V2. If P3<P2, is V2 higher or lower than V1? Explain Homework Equations...

Hellow guys! I find this concept really confusing, if the bulk resistance of a diode is an approximation of the I-V characteristic curve for a diode, Why then is that bulk resistance compared to ac resistances of the same diode at a particular operating in calculated values, seem not to...

State if the following integral converges or diverges, and justify your claim. \int_{-1}^{1} \frac{e^x}{x+1}\,dx I tried using the comparison theorem by comparing it to \frac{1}{x+1} . But for the interval (-1,0) the function is smaller for all x. So I could not conclude whether it...

I was just wondering for the limit comparison test does it matter which function is on the top and bottom?

I am working on an engineering project for college and have run into an unexpected wall. I thought that my approach would work, but I'm not sure if I am getting reliable results and wanted to check on the proper method. I am trying to calculate how long it would take a mass to accelerate...

Hi,I don know if my question will be clear,but I will try it.So,I m wondering how was derive this equation: viscosity=viscosity(known liquid)*density(known from table)*time(liquid will get over one point of Ubelohde viscometer to second point of viscometer(unknown liquid)/density(known...

Homework Statement \sum_{n=1}^{\infty} \frac{7n}{6n^2 ln(n)+2} Determine whether the series converges or diverges.Homework Equations Denominator is growing faster, so the limit as n --> to infinity should equal zerioThe Attempt at a Solution I tried isolating the highest power of the both the...

This may sound very silly and a tad bit hard for me to explain, but here goes! I have experienced and seen how when a lit fire was covered with a container, the oxygen begins to dissipate and it begins to suck things into the space. (I did not light myself on fire!) So I was wondering if...

Dolphins have larger brains than humans. So, why aren't they smarter than humans... or, are they? Are those sneaky Dolphins playing dumb? j/k It's my (very limited) understanding that the cortex is responsible for the higher levels of what we think of as intelligence. So, what's different...

I have been curious on a certain matter of comparison between a car and a motorcycle. if your took a car and a enclosed motorcycle ( for aero and top speed )lets say for hypothetical purposes the car weighed 2000 lbs and had 2000 horsepower, while the bike weighed 500 lbs and had 500...

What is the difference between real photons and virtual photons?

Pretty funny stuff! https://sphotos-b.xx.fbcdn.net/hphotos-ash4/309379_450399368314413_942684559_n.jpg

I'm studying the Milne Universe in two dimensions. The metric is similar to that of Rindler spacetime, but with time and space inverted. ds^{2}=-dt^{2}+t^{2}dx^{2} The Carter Penrose diagram of this spacetime would be the same of Rindler spacetime?

Hey guys, Does anyone have a list of the maximum dimensions of objects that can be carried in various launch vehicles, eg Falcon 9/Falcon Heavy, space shuttle etc? It would be much appreciated!

I'd like to know how to compare two greyscale images with each other using MATLAB. These two images for simplicity sake will both be circles and of different intensities. I need to be able to figure out by what proportion one image's intensity is of the other. For instance with 8-bit...

Note: This is not strictly a homework problem. I'm just doing these problems for review (college is out for the semester) - but I wasn't sure if putting them on the main part of the forum would be appropriate since they are clearly lower-level problems.(Newbie) Homework Statement The...