Example Definition and 845 Threads

This isn't a homework problem. My textbook has an example for this subject and I'm having difficulty understanding it. I follow the example up until the point at which it says, "Notice that 0 < | x - 3 | < (0.1)/2 = 0.05, then " I don't understand why delta was substituted with (what...

Hello. I am having some trouble understanding an integration example we have. I have written it out in the attached pdf. I would be grateful if someone can help me undertand what is going on. I assume you let a = (x-RP)/(√2 ΔRP) da to make the process easier, but I am, not sure how that...

Questions: 1. How can one tell that at time t+dt the velocity of the rocket is an infinitesimal quantity and the velocity of the ejected product a real quantity? 2. Why is for the mass of the rocket not simply written m-dm and why for the mass of the ejected product not written (+)dm?

In an example it says that, if |G| = 15 and G has subgroups A,B of G with |A| = 5 and |B| = 3 , then A \cap B must equal \{e_G\} and the smallest subgroup of G containing both A and B is G itself. Could anyone explain why? Thanks!

Feynman's lecture on physics: chapter 4 derives equation for gravitational potential energy by a "lifting 3 balls" example. The book notes: "But the strange thing is that, in a certain way of speaking, we have not lifted two of them at all because, after all, there were balls on shelves 2 and...

In general I find in books that the path integral approach is an equivalent alternative of the hamiltonian approach for QFT (and for QT in general, but my concern is with QFT). There I usually find that this method is usually developed in a formal way and used to derive Feynman rules, gauge...

Quoting from Wikipedia: "Time dilation would make it possible for passengers in a fast-moving vehicle to travel further into the future while aging very little, in that their great speed slows down the rate of passage of on-board time. That is, the ship's clock (and according to relativity...

This was a question on an online homework for a modern physics class. I had two chances to answer it, but I was wrong both times, so I'm simply curious what the answer is. Homework Statement The Attempt at a Solution (a) Quarks attracted to one another is the strong force (b) A...

Just to make sure that I'm not overlooking anything, is the following an example of a quotient map p: X \to Y with the properties that Y is pathwise connected (i.e. connected by a continuous function from the unit interval), \forall y \in Y: p^{-1}(\{ y \}) \subset X also pathwise connected and...

Hello, I am having trouble confirming that the flux integral is equal to the divergence over a volume. I am making a silly mistake & its just one of those days that I can't eyeball it. Here is the problem. I want to compute the flux integral for \vec{ F}=x\hat i+y\hat j-z\hat k...

Folks, Could anyone give me a working example of a sequence of functions that converges to a function wrt to the supremum norm? Thank you.

I'm still having trouble with the basic foundations of relativity so I am taking a look here at the Galilean transformation. I know the only thing that changes is x' = x-vt Now can someone explain what each variable stands for and can show me how you would do an actual example with...

I have looked it in the Wikipedia, but no simple example. So I am not sure. Is the indexed family of sets just power sets, indexed (indexing means labeling as I understand)? For example the indexed family of sets of set A ={1,2,3,4,5,6} is just the collection of element from power set. A sub 1...

Trying to get the idea behind this, but it's kind of new thinking all this rotational dynamics. The classical example of conservation of angular momentum is when a ballerina pulls in her arms as she spins to spin faster. The angular momentum theorem tells us: I1*α1 = I2*α2 So as she decreases...

I don't understand this estimation lemma example :( We are given the 'curve', And part of the example is showing that the contour integral over the top semicircle C_R tends to zero. Apparently we use the estimation lemma and the fact that, |z^2 +1| \geq |z|^2 - 1 to show, \left|...

I just started learning about group orbits, and wanted to look it up online, because I needed some more clarification. However, stumbling upon this Wolfram's Mathworld entry, I ended up even more confused, especially after reading that example for the permutation group G1. Could someone perhaps...

Homework Statement I am trying to follow a derivation in Jackson - Classical ElectrodynamicsHomework Equations In equation 1.58 (2nd/3rd edition) of Jackson - Classical Electrodynamics he says that by using the fact that \mathbf{\rho} \cdot (\mathbf{\rho} +\mathbf{n})/ | \mathbf{\rho +n|}^{3}...

Homework Statement Might be the sketch most useful first: The prism is sliding horizontally from left to right under condition : S(t)=4*t*t+5*t+1[cm] and the bar OA is rotating, point A is sliding over the prism's slope and point O is the immobilized center of bar's rotation, OA=10cm...

Where did the 50 for the v value come from?

I am having trouble understanding how to find the limit of a function (using the definition of a limit). I have a class example, and was wondering if anyone could walk me through the steps. Homework Statement Using the definition of the limit to show that limx→2(x2)=4 f(x) = x2 c=2 L=4...

I apologize for asking what is no doubt a very basic question. I had thought I understood the example, but re reading the book I realize I did not and can't seem to get to a satisfactory explanation on my own. Greene's example is from pages 46-47 First Vintage Books Edition March 2000...

Discuss the limitation of the galilean transformation,by using an example

What is an example of an absolutely continuous function on [a,b] whose derivative is unbounded? I know that the function f: [-1,1] defined by f(x) = x^2sin(1/x^2) for x ≠ 0, f(0) = 0 is continuous and its derivative f'(x) = 2xsin(1/x^2)-2/xcos(1/x^2) for x ≠ 0, f'(0) = 0 is unbounded on...

Homework Statement for discrete basis vectors {{e_n}}, a state vector |psi> is represented by a column vector, with elements being psi_n = <e_n|psi>. When basis vectors correspond to those with continuous eigenvalues, vectors are represented by functions. Give such an example of a state...

This might look a bit stupid but I have just started beams and I can't understand a part in this example it is to do with finding a general equation of the height at any given point on a tapered cantilever beam can someone please explain

Homework Statement [PLAIN]http://img851.imageshack.us/img851/5741/86853377.jpg The Attempt at a Solution For the long straight wire, the charge per unit length λ is already given, this is distributed on the surface of the wire. The electric field is zero for anything less than r1...

Given the following image of 2 conductors, a negatively charged inner ring and positively charged outer ring, taken from http://www.physicsclassroom.com/class/estatics/u8l4d.cfm" Where are the electrons located in the outer ring? If there was no inner ring, and as the outer is...

Find the expectation value of the potential energy in the nth state of the harmonic oscillator. This is his example 2.5 in the book, he uses a\pm=1/Sqrt[2hmw](\mpip+mwx) to get x=Sqrt[h/2mw](a_{+}+a_{-}) My question how does he do this? I can't seem to make the algebraic manipulations to...

A reaction is Spontaneous means what??a reaction is favorable? let me give an example:-By taking a Balloon and blowing air into it we are imparting Energy to the Balloon as the KE of the air molecules so was this reaction spontaneous? or the reverse is spontaneous i.e leave the balloon and let...

the general form of state space output is y=cx+du which means that output is linear combination of state variables and inputs my question is can we write output in this form when our output is not combination of state variable for example in rlc circuit state variables are vc and IL now if we...

Ok I am only a physics undergrad so if this is obvious I am sorry. I understand the concepts of SR pretty well but one thing has bugged me. In the most basic light clock example used to describe the effects of time dilation, where 2 mirrors are placed 1 ls apart on a moving boxcar with an...

Homework Statement https://www.physicsforums.com/attachment.php?attachmentid=39373&stc=1&d=1317244721 Homework Equations In all honesty I am not sure? The Attempt at a Solution This question was used as a worked example in my first tutorial for Dynamics. The lecturer didn't break it down...

good day, this is the multiplication property of equality rule a * b = b * c but is this the multiplicative equality too: a * x = b thank you so much have a good day asburyparknj

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Homework Statement Let X = R2 with the Euclidean metric and let S = {(x1, x2) : x1^2+x2^2 <1}.Prove that Closure of S ={(x1,x2):x1^2+x2^2<= 1} and that the Boundary of S= { (x1, x2) : x1^2 +x2 ^2=1 } . Homework Equations The Attempt at a Solution I was able to prove all my...

As i know, the metallic structure for example a pure copper metal which is made up of all metal atoms that is the copper atoms actually have all its atom of metallic element bonded together by metallic bonding. Metallic bonding is the electrostatic force of attraction between the positively...

please the exmple for wims

Hey folks, I'm trying to find out if a more luminous, less massive body can orbit a more massive, less luminous body (is this an obvious question?). Can such a thing happen? Can it happen in a binary system perhaps..? By less massive I'd also like to know if it can mean the smaller mass being...

Homework Statement What sampling frequency would you use to sample the following signal x(t) = 3sin(9πt) - 6cos(8πt)Homework EquationsThe Attempt at a Solution let T1 be the period of 3sin(9πt) and T2 the period of 6cos(8πt) T1 = 2π/9π = 2/9 Τ2 = 2π/8π = 2/8 thus, if f1 is the frequency of...

Homework Statement two long cylinders (radii a and b) are separated by material of conductivity (sigma). if they are maintained at a potential difference V, what current flows from one to the other, in a length L? Homework Equations Please see the attachment The Attempt at a Solution...

Homework Statement http://www-thphys.physics.ox.ac.uk/people/JamesBinney/complex.pdf Example 1.2 (Page 6) Homework Equations De Moivre's Theorem, Euler's Formula, and other simple complex number theory formulas The Attempt at a Solution I'm having troubles understanding the format, which...

Hi I found these two definitions of duty cycle: [SIZE="3"]1: The duty cycle of a machine refers to how long it can keep operating before it needs a rest, or what percentage of the time it's designed to be in use. For instance, a machine gun might only be able to fire continuously for 100...

hello to everyone, I have a problem solving a stochastic differential equation of the form: dX/dt=aX²+bX+c+sXn(t), where n(t) is white noise with a mean value equal to 0 and variance equal to one. Does anyone know the solution of this stochastic differential equation or how to solve...

Say you have exp{(\omega)} and \omega has a simple pole show that exp{(\omega)}=exp{(F+)}z^{-1}exp{(F-)} where F+ is holomorphic and F- is antiholomorphic. My basic thought is if \omega has a simple pole then \omega z is holomorphic and on the punctured disk it can be represented by a Laurant...

Hi, Ho do I calculate for the curve line in this graph I understand that I use this equation v = d/t.Could anyone show me an example?

Hi, I've these values: # x y=f(x) 50 1957768251 100 3915542997 150 5873311096 500 19577709464 1000 39155455160 1500 58686574963 2000 78292255800 2500 97888617384 3000 117466340329 3500 137044056081 4000 156491263529 4500 176177759312 These values...

Homework Statement My dad is driving coal. His truck has a limited coal-capacity, and enough fuel. He drives this coal from the central which has enough coal, to farmers that need different amounts. As there are many farmers, he has to drive back and forth several times. He knows all...

Hi there, I time (seconds) and speed data for a journey in a car. I looking to get the jerk profile of the car. Jerk can be derived by taking the second derivative of the speed. Can some please show me an example of how to calculate it. Thank you Some sample data is time speed 1...

Can someone give me an example of a case where kinetic force would be greater than static force? Thanks.

Hi! I started to look into freq response analysis of a cantilever beam using COMSOL. Luckily COMSOL already has an example model "Model Library>> Structural mechanics module>>Dynamics and Vibrations>>rotating blade". While not changing anything in the model and with Omega=0 and Cloris =0, I get...