Delta Definition and 1000 Threads

Prove Lim x^2=9. With the epsilon/delta definition of a limit. x->3 My work so far. For every ε>0 there is a δ>0 such that if 0<|x-3|<δ , Then |x^2-9|<ε so, |(x-3)(x+3)|<ε |x-3|* |x+3|∠ε what do I do from here? My book is not very clear (Stewart Calculus 7ed)...

Homework Statement I need to prove for arbitrary functions φ(x) that: \lim_{\lambda \to 0} \int_{-\infty}^{\infty} \frac{1}{\sqrt{2 \pi} \lambda} exp\left( \frac{-x^{2}}{2 \lambda^{2}} \right) \varphi(x) dx = \varphi(0), which, in the sense of distributions is basically the delta...

Homework Statement Given the delta function -α[δ(x+a) + δ(x-a)] where α and a are real positive constants. How many bound states does it possess? Find allowed energies for \frac{hbar2}{ma} and \frac{hbar2}{4ma} and sketch the wave functions. Homework Equations I know there are three parts of...

If the velocity of the object of 5 kg changed from 5 m/s to 4 m/s. Then is the change in kinetic energy -22.5 J or +22.5J. doesn't change mean final velocity minus initial velocity?

For two body decay, in CM frame, we know that the magnitude of the final particle momentum is a constant, which can be described by a delta function, ##\delta(|\vec{p^*}|-|\vec{p_0^*}|)##, ##|\vec{p_0^*}|## is a constant. When we go to lab frame (boost in z direction), what's the Lorentz...

Find the limit L. Then use the epsilon-delta definition to prove that the limit is L. $\sqrt(x)$ as x approaches 9 I figure out the first part of the question. the Answer is three. Yet I have some difficulty to answer the second part of the question.Thank you Cbarker11

I have been reviewing some details on the Dirac Delta function and I've hit a little bit of a road block with trying to wrap my head around how the Translation/Sifting property of the function is justified. Now according to my text the overall definition is the generalized function with the...

With Δt = γ ( Δt' + v Δx' ) For calculating delta t for stationary twin with values of traveling twin. Is it conventional that velocity (v) outbound is positive and distance (x') is negative. Then at turnaround point sign of velocity changes to negative. And for inbound v is negative and...

Hello guys, I need some serious help for the solution of a problem in Q.M, I'm not so sure if I deal with it properly.. Consider an infinite potential well with the traits: V(x):∞, for x>a and x<-a...

Homework Statement Find the inner product of f(x) = σ(x-x0) and g(x) = cos(x) Homework Equations ∫f(x)*g(x)dx Limits of integration are -∞ to ∞ The Attempt at a Solution First of all, what is the complex conjugate of σ(x-x0)? Is it just σ(x-x0)? And I'm not sure how to...

What is the physical meaning to a bound state with negative energy? As I understand it, this is the case with the delta function potential, which admits only one bound state with a negative energy. If the potential function is identically zero throughout (except at the delta function peak)...

I am struggling to remember how to determine the allowable delta max for a beam. I am currently modeling the bending forces upon a piece of square tubing, and though developing delta max seems rather straight forward, I can not seem to remeber how to determine just how much deflection I am...

Homework Statement Show that ##\frac{1}{\pi}\lim_{\epsilon \to 0^+}\frac{\epsilon}{\epsilon^2+k^2}## is representation of delta function.Homework Equations ##\delta(x)=\frac{1}{2 \pi}\int^{\infty}_{-\infty}dke^{ikx}## The Attempt at a Solution...

I am trying to check whether lim h→0 (R(h)/||h||) =0 or not. I am working in ℝ2. h=h1e1+h2e2** => ||h||=(h1^2+h2^2)^1/2 I am using the definition that (R(h)/||h||)<ε * whenever 0<|h|<δ for all h. Example 1 (R(h)/||h||)=h1h2/(h1^2+h2^2)^3/2 I can see that the denominator dominates...

My book loves to represent the delta function as: δ(r-r')=∫-∞∞exp(i(r-r')k)dk Now I can understand this formula if the integration was over the unit circle since. But this is an integration for which the antiderivative as no meaningful limit as x->±∞

Homework Statement Consider a container with two chambers of the same size separated by a fixed membrane in the middle (permeable only to the ideal solute, but not the solvent). One chamber initially contains 1M of solute, and the other contains 0.5M of solute. Write an equation for the...

I want to calculate the delta V needed to move objects around in a 1-d gravitational field. The relevant equations as far as I can see are the Tsiolkovsky equation, \Delta V = v_{ex} \ln\left(\frac{m_0}{m_1}\right) and the equation for calculating escape velocity. v_e = \sqrt{\frac{2GM}{r}}...

Prove that a set $A\subset\mathbb{R}^n$ is (Lebesgue) measurable $\iff$ there exist a set $B$ which is an $F_{\sigma}$ and a set $C$ which is a $G_{\delta}$ such that $B\subset A\subset C$ and $C$~$B$ (C without B) is a null set. $F_{\sigma}$ is a countable union of closed sets, and...

Homework Statement I'm specifically having trouble with taking the Fourier transform of f(t) in order to sketch F(w) and also to move on with the rest of the problem. Homework Equations f(t) = (5+rect(t/4))cos(60pi*t) mixed_signal = cos(60pi*t) The Attempt at a Solution I attempted to...

Homework Statement OK so I'm doing a course on Signals and Systems and I'm taking inverse z transforms using residue integration. One particular formula in complex integration made me think a bit. \oint{\frac{f(z)}{z-z_0} dz} = 2\pi jf(z_0) This looks eerily similar to the definition...

I have seen several thermodynamic equations represented with the lowercase delta, \delta, and the standard d to represent an infinitesimal change. For example, the change in internal energy is denoted in Wikipedia as: dU = \delta Q + \delta W Them the equation for \delta Q : \delta Q =...

I have a few confusions related to the delta configuration of a transformer (single-phase transformers used to make a 3-phase transformer): 1) In a closed delta, the windings are connected such that H2 end of one winding is connected to H1 of the other winding. What will happen if one of the...

Hello, I have had this question for awhile now. What is the difference a delta baryon and a nucleon? they seem to have the same quark composition? Thanks in advance.

Homework Statement This is just an example, not a specific problem. So if I have ∫σ(sinx), for example, and my limits of integration are, for example, 1 to 10, what I need to do to solve that is to find a value of x that would make the argument of the delta function 0. So for sinx, 0 makes...

Homework Statement The Potential V(r) is given: A*e^(-lambda*r)/r, A and lambda are constants From this potential, I have to calculate: E(r), Rho(r) -- charge density, and Q -- total charge. Homework Equations The Attempt at a Solution I know that E(r) is simply minus...

Homework Statement The equation and data to which the question refers is in the attachment. I am just trying to do part (a) of the question at the moment: Calculate ΔG and K, the equilibrium constant, for this reaction at 298 K. Homework Equations I would have thought that I would need...

In the double delta function potential well, where one delta function ( -αδ(x) ) is at -a and one at +a, if the energy is less than zero, there can be either one or two bound states, depending on the magnitude of α...if α is large enough, there can be two bound states, but if α is small, there...

Hi guys! There is something I fail to understand in normalising wave functions to dirac's delta. Let's take the free particle solution as an example. Please note that my question is not about using the solution as much as about undestanding the concept. ----- The situation The general...

My question concerns the delta++ baryon. I understand that the rest mass of quarks makes up a very small percentage of the total mass of a baryon, but I don't understand exactly what it is about delta ++ (uuu) which makes it have greater rest mass than a proton (uud). If anyone can explain...

Homework Statement Prove this theorem regarding a property of the Dirac Delta Function: $$\int_{-\infty}^{\infty}f(x)\delta'(x-a)dx=-f'(a)$$ (by using integration by parts) Homework Equations We know that δ(x) can be defined as...

Does the Dirac delta have a residue? It seems like it might, but I don't know how to attack it, since I really know very little about distributions. For example, the Dirac delta does not have a Laurent-expansion, so how would you define its residue?

Hi All, I found (Wikipedia page on Helmotz's decomposition theorem) the follwoing equality, which puzzles me: $$\delta(x-y) = - (4 \pi)^{-1} \nabla^{2} \frac{1}{\vert x - y \vert}$$ I am not sure I understand, the r.h.s seems to me a proper function. The page mentions this a sa position...

What does the Dirac Delta Function do? ##\delta^3(\vec{r})## How do you evaluate it? What are its values from -inf to +inf?

Hey there, I'm new to this forum. Today I thought I would brush up on my calculus. I would just like to know if my method is correct. Is there an easier way to prove this ? By the way, it's my first time using LaTeX, so bear with me. I am trying to prove the following : \lim_{x\rightarrow...

Can someone explain the following profound truth: \frac {\partial f(x)}{\partial f(y)} =\delta(x-y)

predict the sign for delta Ssys CH3CH2CH3(g) +5O2(g)---> 3CO2(g) + 4H2 Homework Statement predict the sign for delta Ssys CH3CH2CH3(g) +5O2(g)---> 3CO2(g) + 4H20(l) The same question for N205(g) --> NO2(g) + NO3(g) Homework Equations The Attempt at a Solution I said the...

Homework Statement (a) Show that that δ(a-b)=∫δ(x-a)δ(x-b)dx (b) Show that ∂/∂x θ(x) = δ(x) where θ(x) is the heaviside step function (0 for x<0, 1 for x>0) (c) Show that ∫(-inf to inf) δ(x) f(θ(x))dx=∫(0 to 1) f(y)dy Homework Equations The definition of the delta function...

I seem to be having trouble with multivariable epsilon-delta limit proofs. I don't have a very good intuition for how \epsilon relates to \delta. For example: Prove \lim_{(x,y) \to (0,0)}\frac{2xy^2}{x^2+y^2} = 0 There are probably many ways to do this, but my teacher does it a certain way...

Hi, From the basics of 3 phase power, I believed that if you had a delta source which had Line Voltages and Phase Voltages of 100V, if you converted this into a star source, the Equivalent Star Line voltage would still be 100V and the equivalent star phase voltage would then be 100V/sqrt(3)...

It's been quite some time now since I decided to stop self-studying physics and to pay more attention to the math behind. I'm working towards gaining an understanding of 100% rigorous mathematics for now. One thing that has always bothered me is the Dirac delta function. What I want to know...

E is finite and V is infinite, So T should be negative infinite

Homework Statement Good day. May I know, for Dirac Delta Function, Is δ(x+y)=δ(x-y)? The Attempt at a Solution Since δ(x)=δ(-x), I would say δ(x+y)=δ(x-y). Am I correct?

Homework Statement It's a projectile problem. Basically, you launch a projectile starting from a height ΔY (0.5 m) at speed V0 at an angle θ. Then after time T, the projectile then hits the ground (0m) and sticks to the ground, traveling distance ΔX. The question goes if you are given ΔX...

Homework Statement I need to prove that 1/n has a limit of zero using the following definition: The statement that the point sequence p1, p2, . . . converges to the point x means that if S is an open interval containing x then there is a positive integer N such that if n is a positive...

Homework Statement For fixed m ≥ 1, let ##\epsilon(i,j)## denote the m x m matrix ##\epsilon(i,j)_{rs} = \delta_{ir}\delta_{js}##, where i,j may denote any integers in the range 1 ≤ i,j ≤ m. (a) When m = 4, write out all ##\epsilon(i,j)## explicitly and label them correctly. The attempt at a...

I know delta means change , but I don't what the difference between Δv/Δt vs dv/dt is ? I am at the noob end of calculus so trying to grasp how to interpret things like dv/dt or what what dv would mean if it were standing alone. TIA

Hello, I would like someone to give me some help or clarification relating to the conversion from a delta to star source. I understand that in star, Line Voltage is sqrt(3) times the phase voltage, and line voltage also leads phase by 30°. I also understand that Line and Phase currents are the...

From what I can tell, it seems that 1/x + δ(x) = 1/x because if we think of both 1/x and the dirac delta function as the following peicewise functions: 1/x = 1/x for x < 0 1/x = undefined for x = 0 1/x = 1/x for x > 0 δ(x) = 0 for x < 0 δ(x) = undefined for x = 0 δ(x) = 0 for x > 0...

Homework Statement Find δ (which is the input tolerance): lim (9 - 4x2)/(3 + 2x2) = 6 x→-1.5 Homework Equations |f(x) - L| < \epsilon |x - a| < \delta The Attempt at a Solution lim (9 - 4x2)/(3 + 2x2) = 6 x→-1.5 I need to get to: |x-(-1.5)| < \delta = |x + 1.5)| <...