Comparison Definition and 393 Threads

Hi everyone i am new to the forum. I am looking forward to a MSc in theoretical physics and have been offered place at Utrecht and Glasgow university. Unfortunately neither of the universities have a very detailed course outline at their sites (or its just my fault). I am interested in high...

Homework Statement Determine whether the series is converging or diverging Homework Equations ∞ ∑ 1 / (3n +cos2(n)) n=1The Attempt at a Solution I used The Comparison Test, I'm just not sure I'm right. Here's what I've got: The dominant term in the denominator is is 3n and cos2(n)...

Homework Statement I'm working on a problem in Design and Analysis of Experiments by Dean and Voss. It's Chapter 10 question 11 part c. We have an experiment with 2 treatment factors (each with three levels) and 1 blocking factor (with four levels. It's a randomized complete block design so...

Hi All, Using (Mirror + Translation in 2D). I see that Diamond and Center Rectangular Lattice in 2D has the same Symmetry i.e: 1)Horizontal Mirror Plane 2)Vertical Mirror Plane 3)2-Fold Rotation Axis. and Diamond has Smaller Area. Then why we say Center Rectangular has higher Symmetry and we...

Hi I am trying to compare which of the (2) models has the greatest stability longitudinaly. I have the COG height and longitudinal (axle split) Model A has it COG closer to the centre of the axles (longitudinal - further from rear axle 1,487l) but sits much higher (2,537 above axle centre) Model...

Homework Statement Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B. Both carts start from rest. The velocities vA and vB of the bodies at the end of distance D are...

Homework Statement The same constant force is used to accelerate two carts of the same mass, initially at rest, on horizontal frictionless tracks. The force is applied to cart A for twice as long a time as it is applied to cart B. The work the force does on A is WA; that on B is WB. Which...

Hi everybody, my question is not properly about CFD but mainly about Fluid Dynamics itself. I have performed a RANS simulation of a round jet of methane and air and now I'd like to compare those results to some experiments. Unfortunately there aren't papers about experimental data for...

okay, so I know that light is faster than sound, and we can prove it with many visuals, but can y'all give examples of speeds through the same medium. For example, I know that the speed of sound is 343 in room at 200 C

I have a heat exchanger with water/air as medium and we test it in a facility where we cycle the water temperature between 25 to 95 degrees Celcius with a cycle time of 5 minutes for thermal fatigue. Our customer require the testing to be between 5 to 95 degrees instead with 3 minute long...

I was reading a rapid reader called The Canterville Ghost by Oscar Wilde. According to that US believed less in ghosts in comparison with UK. So a question arose in me that why not survey people here and discuss. I know Halloween is celebrated there in US. So they also do some scary things. My...

In my textbook it says if you are comparing limn->infinity of an/bn an>0 and bn>0 for the limit comparison test to apply. It says nothing about "an" having to be greater than "bn", so as long as both are positive for each term I can use the limit comparison test right? It isn't like the...

Homework Statement Use the limit comparison test to prove convergence or divergence for the series sum from n=1 to infinity for ((5n^3)+1)/((2^n)((n^3)+n+1)) Homework Equations The limit comparison test says that if you have two positive series, sum An and sum Bn, let C=lim n to infinity of...

Homework Statement Use the limit comparison test to show the series converges or diverges: Sum from n=1 to infinity of ((5n^3)+1)/((2^n)((n^3)+n+1)) Homework Equations suppose Sum An and Sum Bn are two positive series. Let lim as n goes to infinity of An/Bn = c: 1) if 0<c<inifinity then either...

The question asks whether the following converges or diverges. \int_{0}^{\infty } \frac{\left | sinx \right |}{x^2} dx Now I think there might be a trick with the domain of sine function but I couldn't make up my mind on this. I tried to compare it with 1/x^2, (sinx)/x, and sinx. I actually...

Homework Statement Use the limit comparison test to check for convergence or divergence: Sum from n=1 to infinity of ((2n)^2+5)^-3 Homework Equations let lim n to infinity of An/Bn = c 1) if 0<c<infinity then either both converge or both diverge 2) if c=0 and sum Bn converges, so does sum An...

\int_{0}^{\infty} \frac{x^2 dx}{x^5+1} The question asks whether this function diverges or converges. I have tried to do some comparisons with x^2/(x^6+1), and x^2/(x^3+1) but it didn't end up with something good. Then I decided to compare it with \frac{x^2}{x^4+1} Since this function...

I simplified a trig equation to \theta=\Big\{sin^{-1}(\frac{1}{2})+2\pi k\Big\}\; and \; \Big\{\pi-sin^{-1}(\frac{1}{2})+2\pi k\Big\} Whereas the book simplified it to \theta=\pm\frac{\pi}{6}+\pi k Obviously these answers encompass the same set of values, with the book's answer being much...

Homework Statement Two blocks with different masses are in contact on a frictionless surface. A force, Fp can be applied to either block. If the magnitude of Fp is the same on both cases, the force exerted by the heavier block on the lighter box is A) The same B) Greater when force Fp is...

Dear Friends! Is weighted mean greater than mean? Actually i need to prove (c-b)f(a)+(b-a)f(c)>(c-a)f(b) when when f is continuous and strictly increasing in [a,c],where a<b<c.

K≥0 ∑ ((sqrt(k)+2)/(k+5)) I am trying to prove that this diverges. The divergence test is inconclusive. Now I am left with a great option of a comparison test. I'm not quite sure what to compare it with, but I know I need to compare it with something smaller (denominator is larger) that...

Homework Statement Let truncn(L) = {w: wv exists in L, |v| = n} Show that trunc is regular if L is regular. The Attempt at a Solution By the definition of regular languages, L is regular if we can come up with a regular expression or a DFA for it. This question confuses me because what if...

Question : Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor R = 10.0 Ω is found to be 58.3 cm, while that with the unknown resistance X is 68.5 cm. Determine the value of X. Isn't the question wrong? I've searched for it...

[Mentor's note: this post does not use the homework template because it was originally posted in a non-homework forum. It was moved here because it had already received some help.] ---------- Weiping lifts a rock with a weight of 1.0 N through a height of 1.0 m, and then lowers it back...

Please look at pictures. I am wondering for (d). Why is the answer the second one? To which structure in Table 3.1 should I compare it to? I compare the first one to CH3CO2-. What about the second one?

Hello PF! I've come here for help again. I am entering as a freshman this fall, and I really, really want to participate in a research as soon as I can. However, I am aware of my lack of knowledge in physics, research techniques and utilities and such. What can I do to prepare for research? I...

Hey guys I've got an assignment. I need a comparison between a normal conductor and a semiconductor and why a classical understanding isn't enough to explain how an SC works. Also are there any electrical properties of an SC besides decreasing resisitivity at higher temps?

I'm trying to find if this series converges or diverges using the comparison test: and the answer goes: My problem is, I am not sure how to go from 1/2^(n+1) to 1/2(1/2)^n. can you please explain that to me

Homework Statement http://i.minus.com/jhPgz49XLoB3Z.png Homework Equations Strength of acid depends on conjugate stability. The Attempt at a Solution Why can't the answer also be 4? Both have the same number of oxygens attached, each of which exerts an inductive effect. The...

Homework Statement Use the comparison test to show that the series converges, and find the value it converge to by using partial fractions. ∑ n=1 -> ∞: \frac{2}{n^2 + 5n + 6} Homework Equations The Attempt at a Solution The series can be written as 2 * ∑ n=1 -> ∞...

Homework Statement I did a 'three point bend test' and a 'tensile test' on the material as-rolled Aluminium. I then messured and calculated the proepties of the metal and compared it with the literature values found on a CES software. Unfortunately, I can find significant differences for...

Hello, Thanks so much for all the previous help. I will probably be using this forum a lot this semester because my textbook is not very helpful. So thank you in advance. I am trying to create a comparison table of CE CC and CB amplifiers to help me study. However, I cannot find the...

Homework Statement Use $$\sum\limits_{n=1}^∞ \frac{1}{n^2}$$ to prove by the comparison test that $$\sum\limits_{n=1}^∞ \frac{n+1}{n^3} $$ converges.Homework Equations $$\sum\limits_{n=1}^∞ \frac{n+1}{n^3} \equiv \sum\limits_{n=1}^∞ \frac{1}{n^2} + \sum\limits_{n=1}^∞ \frac{1}{n^3} $$ The...

Homework Statement $$\sum\limits_{n=1}^∞ \frac{1}{n√(n)} $$ Since $$ \frac{1}{n√(n)} \equiv \frac{1}{x^{3/2}} $$ this is a convergent p-series. But, when I attempt to prove this by the limit comparison test with known convergent series such as $$\sum\limits_{n=1}^∞ \frac{1}{n^2}$$ ex...

Hey, not too sure about what function i would compare this integral from 1 to infinity of (3x^3 -2)/(x^6 +2) dx. I also have to show that it converges. Thanks!

Homework Statement Concentrated forces are to distributed forces as particles are to A. Objects B. Rigid bodies C. Planets D. Solids Homework Equations The Attempt at a Solution I say B I have looked up the definition of a rigid body and it seems a particle can be...

So how much denser than is a neutron star than an atom? Is it called a neutron star because electron's orbital effect no longer exists/acts the same, so as to no longer cause 99.99% of everything to be space?

Consider both UART and SSI transmission of data at a Baud rate of 10Mbps. Are they at equal speeds as an entirety, or is one faster than the other? I understand that the Baud rate is the rate of transmission, however, once the bits have been transmitted they undergo further steps to be processed...

Homework Statement Does \sum_{n=1}^{\infty}a_n where a_n = \frac{(n+1)^{1/3}-n^{1/3}}{n} converge or diverge? Homework Equations The Attempt at a Solution The ratio test is inconclusive, as is the root test. The limit is equal to 0, but that doesn't say much. I've tried to find...

Homework Statement Let ##\displaystyle a_n=\frac 1 2+\frac 1 3+...+\frac 1 n##. Then A)##a_n## is less than ##\displaystyle \int_2^n\frac{dx}{x}##. B)##a_n## is greater than ##\displaystyle \int_1^n\frac{dx}{x}##. C)##\displaystyle \lim_{n\rightarrow \infty} \frac{a_n}{\ln n}=1##...

Homework Statement Use the Limit Comparison Test to determine if the series converges or diverges: Ʃ (4/(7+4n(ln^2(n))) from n=1 to ∞. (The denominator, for clarity, in words is: seven plus 4n times the natural log squared of n.) Homework Equations Limit Comparison Test: Let Σa(n) be the...

Hi, I'm studying http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Comparison_of_interpretations but have trouble with the apparent differences of the key concepts: * deterministic - unique history * wavefunction real - hidden variables - counterfactual definiteness I...

I was wondering if there is a generalization of the following (roughly stated) theorem to n-dimensional systems: Given some restrictions on the functions f and g \in \Re, let y_s(t) and x_s(t) \in \Re be solutions to the initial value problems: \dot{x}(t) = f(x,t), x(t_0) = x_0\\...

Does anyone know of an article that has a good in-depth, side by side comparison of DFB edge emitting lasers and VCSEL lasers? From my research it seems to me that the VCSEL papers are all trying to justify why laser production should shift towards VCSEL, and mostly list the advantages over an...

Hi! I'm having problems understanding the last step of a derivation for a version of a theorem of Gromov's we had in class: In short, the proof takes the Riemannian universal covering (\tilde M, \tilde g, \tilde p) of (M, p) and uses a short basis (\gamma_1, \gamma_2, ...) of the deck...

Hi, Which of ZnS and CdSe will have the larger band gap energy, explain. The answer is given as Zinc sulfide will have a larger band gap energy than cadmium selenide. Both are II-VI compounds, and Zn and S are both higher vertically in the periodic table than Cd and Se. In moving from...

If we have two sequences and the ratio of their limit is greater than zero, why does this mean that they either both converge or diverge? I don't understand why the test works. Also, what about lim[(1/x)/(1/x^2)] = lim x = ∞? The series of 1/x^2 converges but series of 1/x diverges...

Homework Statement Determine whether Ʃ(n from 1 to infinity) ln(n)/n^3 converges or diverges using the limit comparison test. Homework Equations I must use the limit comparison test to solve this problem-not allowed to use other tests. The Attempt at a Solution I know that the...

1. Homework Statement [/b] Use the direct comparison test to show that the following are convergent: (a)\int_1^∞ \frac{cos x\,dx}{x^2} I don't know how to choose a smaller function that converges similar to the one above. The main problem is i don't know where to start. A simple...

What is the different between HSLA and tool steel in term of properties, price and application