Comparison Definition and 393 Threads

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...

Homework Statement determine whether the series diverges or converges (∞,n=1) ∑ (n2 - 1)/(3n4 +1) Homework Equations The Attempt at a Solution (∞,n=1) ∑ (n2 - 1)/(3n4 +1) an = (n2 - 1)/(3n4 +1) i thought bn should be n2/3n4 = 1/3n2 lim n-->∞ an/bn = (n2 - 1)/(3n4 +1) * 3n2 lim n-->∞...

Hi, I would like to measure the signal noise in a tv cable after introducing a splitter and compare it with the original signal. Keeping in mind the bandwidth frequency of the tv cable signal transmission, what kind of instrument do I need? Oscilloscope perhaps? At what speed? I don't know...

Hi This a question from one of my exam papers.I searched all over internet but couldn't find any article or information source comparing atmel vs PIC in following manner. all i could find was threads talking about which is better.none of them discussed the matter with respective to following...

Homework Statement The problem is to show that \int_1^x \frac{| \sin(t) |}{t} dt \underset{x \rightarrow \infty}{\sim} \frac{2}{\pi} \log(x). The integral is (in case it is important) a Lebesgue integral. Homework Equations A theorem is stated which says (I do not currently have the...

Hi This is my first post, and I have a lot of ideas to talk about I'll start with this one: What would the difference be between a thermonuclear explosion and an antimatter explosion, of equal yield (say 2 megatons each), and similar location and weather? I think that the each would have a...

Homework Statement Determine whether or not the integral from 0 to 1 of (5ln(x)) / ( x^(3/2) ) converges or not. Homework Equations The Attempt at a Solution I just need to know which end of the integral they are talking about. As x=>0, y=>-infinity. As x=>1, y=>1. I'm assuming...

Homework Statement Determine whether or not the improper integral from 0 to infinite of (e^x)/[(e^2x)+4] converges and if it does, find it's definite value. Homework Equations The Attempt at a Solution I missed the lecture on the Comparison Test, so I'm essentially useless. I...

Homework Statement Suppose that the instantaneous velocities of two positive point charges are parallel. Compare the electric and magnetic forces. Show that the ratio of the magnetic force (Fmag) to the electric force (Felec) is: Fmag/Felec = v1*v2/c^2 Where v1 and v2 are the velocities of...

in 2's complement the negative of 1 is "111". but it also signifies 7 in decimal. how does this -ve 1 is differ from 7? thanks

Homework Statement The summation of n/lnn from n=1 to infinity Homework Equations Ratio and Comparison test The Attempt at a Solution http://i55.tinypic.com/2jxuue.jpg Alright so the way labeled "right way" on the picture is the right way according to the book but isn't the...

Hi, I am experimenting with traction controlling of wheels. I have to calculate the speed difference in two wheels (driven and non-driven). I am thinking of these options: 1. Generate pulse train using optical encoder -> binary counter -> D/A converter -> Take voltage difference using OP...

Just a general question, but I find it hard to come up with a b[n] to compare to a[n]. When the book does it, they come up with stuff to compare to a[n] that I would have never thought of. Is there any criteria, things to look for, etc., for coming up with a b[n] to compare to a[n]?

Homework Statement \sum_{n=1}^\infty \frac{1+4^n}{1+3^n} where a_n= \frac{1+4^n}{1+3^n} and b_n= \frac{4^n}{3^n} Homework Equations I know how to do this problem, you take the limit as "n" goes to infinity of a_n/b_n ... which after a good amount of algebra ends up being 1...

Finding "a" and "b" in an infinite series limit comparison test Homework Statement \sum_{n=1}^\infty \frac{\sqrt{n+2}}{2n^2+n+1} How do I identify my a_n and my b_n? In this particular problem you need to use the Limit comparison test which is your "a_n" divided by your "b_n". I...

Homework Statement show whether \sum (n+5)/(n3-2n+3) is convergant of divergant Homework Equations limit comparison test, lim an/bn = c where c > 0 The Attempt at a Solution an is given let bn = n/n3 so then: lim (n+5)/(n3-2n+3) n/n3 = lim (n+5)n3 /...

Homework Statement Alpha Centauri is about 4 light years from the Earth. If you were to travel to Alpha Centauri and back at the speed of the electron that you calculated in question A (0.780c), how much would you age compared to an observer on Earth? Homework Equations There equations...

1. The problem statement: Prove that 0\leq2x^2 - 3xy + 2y^2 2. These are the axioms we are permitted to use: 01) Exactly one of these hold: a<b, a=b, or b<a 02) If a<b, and b<c, then a<c 03) If a<b, then a+c < b+c for every c 04) If a<b and 0<c, then ac<bc. The Attempt at...

Hello, I'm new to this forum so I don't really know if this is the correct section for this question, but I couldn't find anything that fits better. I'm in my last year in school and writing a program for an extended essay (at least that is what google tells me is the translation for the...

Homework Statement question given is 1 + 1/1! + 1/2! + 1/3! + · · · the question need to be compared with another equation so how to get the second equation? Homework Equations n/a The Attempt at a Solution i duno homework to startT.T

Say you had a color picked out and a list of different colors that you wanted to find the closest matching color from. Is anyone aware of some formula to do this for computer RGB colors?

I have plastic, metal and rubber parts that are compatible with ethyl alcohol (they are regularly washed in a bath of ethyl alcohol). I’m looking for a substitute solution to wash these parts and I am considering denatured alcohol, however, I’m concerned that the denaturing ingredients will...

Homework Statement Explain why the Direct Comparison Test allows us to use the inequality Ln n < n^(1/10) even though it is not true for a great many n values. Homework Equations The Attempt at a Solution I looked at the graphs of Ln (n) vs. n^(k)

I have a fairly basic (I hope) question - please note that the values given are just to make the problem easier to comprehend: Given: I'm heating, via convection, a constant sized spherical mass (Let's say m=1g) with a consistent surface area (Let's say SA = 1cm^2) at a constant...

Homework Statement Finally done with stupid improper integrals (calc 2 over summer is hard work, moving super fast) and now I'm sequences and series and what have you. I have another comparison test problem Instructions are to find out if sequence converges or diverges, and find limit if it...

Homework Statement I'm just curious as to how to think about the following form of equation. Homework Equations \int_{3}^{\infty } \frac{1}{x + e^x} \,dx The Attempt at a Solution What you're trying to do is to test it; \frac{1}{x \ + \ e^x} \ < \ \frac{1}{x} \frac{1}{x}...

Hi, I just can't understand the basics with BZ. How do I find the shortest distance to the BZ boundary, how do I compare the electron energy between the last electron in the 1st BZ with the first electron in the 2nd BZ? I think I need a visual how to calculate these things, does anyone...

Size comparison of WASP-12b (gray) with Jupiter. http://d.yimg.com/a/p/afp/20100524/capt.photo_1274732261799-1-0.jpg Reference: http://en.wikipedia.org/wiki/WASP-12b" http://en.wikipedia.org/wiki/WASP-12" [PLAIN]http://news.yahoo.com/s/afp/20100524/ts_alt_afp/usscienceastronomy"

Hi guys, I'm new to the forums and hope someone can help with this. Homework Statement Compare the modulation techniques used by 2 different applications, giving reasons for their use. Use data tables, diagrams and any other sources to help Homework Equations None The Attempt...

hi, i measured the emission spectrum of an LED with a monochromator connected to a PMT tube. the spectrum was measured at four different gain levels on the PMT. i want to check the PMT's linearity at the different gain level, so i want to compare the four data sets and check their...

Homework Statement int (e^-x)/(x)dx from 0 to infinity Determine if integral is convergent or divergent2. The attempt at a solution I assume because the bottom limit is 0 and there is an x in the bottom of the integral that this is going to be divergent but I still have to use the...

Hi, so I have a question that has been plaguing me for the longest.. I am a high school senior and I hope to Major in Physic when I enter college, yet I am torn between two schools. Georgia Institute of Technology vs. Jackson State University Now, I can be pretty sure of the obvious...

Can the limit comparison test work on alternating series? I looked at the conditions online and it said that the series a_n and b_n must be > 0 in order to use it. To be specific it said, "Suppose that a_n > 0 and b_n>0 for all n> or = to N (N a positive integer)." I asked my teacher about this...

Homework Statement Determine if the following is improper and convergent, improper and divergent, or proper \int \frac{dx}{\sqrt[3]{x^2 - 7}} from 8 to infinityThe Attempt at a Solution Since I don't know how to integrate...

what are the main differences between the 2nd generation (GSM) system and the 4th generation, in terms of: -the type of modulation used. -multiplexing with the base station. -bit rate and bandwidth given for each supscriber. - the complexity of the system. if you could provide links for...

Using the equation Force = Pressure x Area. How much energy would be released from an iron tube 48” long with an inside diameter of 2.1” and outside diameter of 3”. Wall thickness would be .9”. With 8500psi inside. Maybe I calculated it wrong but I got 1.1 million pounds of force released. Once...

the frequency of radiation emitted when electron and positron are annihilated in the moving carriage is more than the the frequency of radiation emitted when the same experiment is done on railway platform .Is it not enough to decide that the motion of the train is real while platform motion is...

1. Homework Statement The electric field strength 7.79 cm from a very long charged wire is 2660 N/C. What is the electric field strength (in N/C) 12.7 cm from the wire? 2. Homework Equations E= (9*10^9) Q/ r^2 3. The Attempt at a Solution i have energy. so is tried to solve...

Homework Statement Use a comparison to determine if the improper integral converges or diverges. If the integral converges, give an upper bound for the value. Integral of d(theta) / (theta^3 + theta)^1/2 from 1 to infinity Homework Equations N/A The Attempt at a Solution I'm...

I'm having an extremely hard time understanding direct/limit comparison tests, and i will post some questions so you guys can attempt to help me. integral from 0 to pi of: dt/[sqrt(t) + sin(t)] and integral from -infinity to infinity of: dx/[ex + e-x] I cannot show my work because i...

Could anyone help me on this question? Is it true that \sum_{k=n+1}^{2n}\left(\begin{array}{c} 2n\\k\end{array}\right)x^{k}\left(1-x\right)^{2n-k}\leq2x for any x\in(0,1) and any positive integer n? Any help on that will be greatly appreciated!

Homework Statement Draw a clearly labelled “Minkowski spacetime” diagram illustrating two events ((1) a farmer firing his laser gun at his cow, which is sitting along his positive x-direction, and (2) the cow dying) as observed by two observers (S at rest in the farmer’s and cow’s frame, and...

When we are taught relativity we never seem to be asked to consider how the configuration of objects in frames moving relative to ours actually got there. It just seems that we imply that is the way they always were and so an actual congruence measurement of direct comparison in the same frame...

I am planning to do some simulations using path integral molecular dynamics approach. I have never used it before, so I would like to have some information concerning packages that are used for that kind of simulations. I am aware of PINY and CPMD packages for PIMD. Which one is better? Are...