Value Definition and 1000 Threads

I am reading Cesar E. Silva's book entitled "Invitation to Real Analysis" ... and am focused on Chapter 4: Continuous Functions ... I need help to clarify an aspect of the proof of Theorem 4.2.1, the Intermediate Value Theorem ... ... Theorem 4.2.1 and its related Corollary read as follows...

Question: I first knew that this would be a series circuit setup, there the current all around the circuit would be the same. It's given that when it's a open circuit, p.d. across the output is 4000V hence the emf is therefore 4000V. When it gets connected to a load resistor, the voltage...

This is the problem itself shown below And this is what I have tried, I get an answer of 29 ohms Would you agree?

Here are a couple of questions that I have been trying to answer and had a go at it. Not sure if I answered some incorrectly so was hoping to get some guidance For this one I have tried to make use of Kirchhoff's 2nd law to help me, but this is what I have ended up with when using it...

By carrying out accurate measurements on the amount of deflections observed by the electrons on the electric field strength or magnetic field strength, Thomson was able to determine the value of e/me as... e/me = 1.75 10^11 C kg^-1 would this be a correct understanding of this para- "This para...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 3: Continuous Functions on Intervals and am currently focused on Section 3.1 Limits and Continuity ... ... I need some help in understanding the proof of Theorem 3.16...

I am reading Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 3: Continuous Functions on Intervals and am currently focused on Section 3.1 Limits and Continuity ... ... I need some help in understanding the proof of Theorem 3.16...

given $|y+3|\le 4$ we don't know if y is plus or negative so $y+3\le 4 \Rightarrow y\le 1$ and $-(y+3)\le 4$ reverse the inequality $ y+3 \ge -4$ then isolate y $y \ge -7$ the interval is $-7 \le y \le 1$

Does it make sense to just talk about the average value of a function without specifying the range over which the average is taken? It seems a common occurrence in discussions of waves to just mention that the average value of the complex exponential ##e^{ix}## is zero. But it will be zero only...

Let f be the function defined by $f(x)=\dfrac{\ln x}{x}$ What is the absolute minimum value of f a, 1 b. $\dfrac{1}{e}$ c. 0 d. e e. none ok I assume we take the derivative and then set it to zero $\frac{1-\ln\left(x\right)}{x^{2}}=0$ $x=e$

D={(x,y)∈ℝ2: 2|y|-2≤|x|≤½|y|+1} I am struggling on finding the domain of such function my attempt : first system \begin{cases} x≥2y-2\\ -x≥2y-2\\ x≥-2y-2\\ -x≥-2y-2 \end{cases} second system \begin{cases} x≤y/2+1\\ x≤-y/2+1\\ -x≤y/2+1\\ -x≤-y/2+1\\ \end{cases} i draw the graph and get the...

This is the equation given. I attempted to use Radial Equation, obtained from separating variables, to solve for ##E_1##.

Hi all I was hoping someone could help shed some light clearing some doubt on 2nd Moment of Area. I know that if i had a beam that was loaded then the top of the beam would experience compressive forces. As i moved down towards the neutral axis these compressive forces would become zero. And...

a) Proof: By theorem above, there exists a ##a \in \mathbb{R}## such that for all ##x \in I## we have ##f'(x) = a##. Let ##x, y \in I##. Then, by Mean Value Theorem, $$a = \frac{f(x) - f(y)}{x - y}$$ This can be rewritten as ##f(x) = ax - ay + f(y)##. Now, let ##g(y) = -ay + f(y)##. Then...

Let us say that we have a stellar object so its total velocity is defined as $$ v_{tot} = v_{pec} + V_{rec}$$ Where $$V_{rec} = H_0r$$ and $$V(z) = \frac{cz}{1+z}[1+\frac{1}{2}(1-q_0)z - \frac{1}{6}(1-q_0-3q_0^2+j_0)z^2]$$ for small z.So my first question is what is the $z$ value here? Is...

Hello, I hope you are very well ! I have a physics practical test where I have to find the gravitational acceleration with the Atwood machine: I've found 9.27 m/s² and have to say what could have caused this slight gap. They say that there is no friction in this experiment. I can't really...

ok image to avoid typo... try to solve before looking at suggested solutions ok I think you could do this by observation if you are careful with signs

Let f be a function twice-differentiable function defined on [0, 1] such that f(0)=0, f′(0)=0, and f(1)=0. (a) Explain why there is a point c1 in (0,1) such that f′(c1) = 0. (b) Explain why there is a point c2 in (0,c1) such that f′′(c2) = 0. If you use a major theorem, then cite the theorem...

My solution is not the same, it has an additional *2 factor and i can't see any mistakes.

Given that operator ##S_M##, which consists entirely of ##Y## and ##Z## Pauli operators, is a stabilizer of some graph state ##G## i.e. the eigenvalue equation is given as ##S_MG = G## (eigenvalue ##1##). In the paper 'Graph States as a Resource for Quantum Metrology' (page 3) it states that...

I am struggling to figure out how to calculate the expectation value because I am finding it hard to do something with the exponential. I tried using Euler's formula and some commutator relations, but I am always left with some term like ##\exp(L_z)## that I am not sure how to get rid of.

This paper just came out with a new measurement of the Hubble constant based on the technique of gamma ray attenuation. The result is consistent with the lower (CMB-based) value. Interestingly, they also do a joint analysis of several non-CMB techniques (BAO+BBN+SN+γ-ray attenuation), and find...

I am reading "Complex Analysis for Mathematics and Engineering" by John H. Mathews and Russel W. Howell (M&H) [Fifth Edition] ... ... I am focused on Section 3.2 The Cauchy Riemann Equations ... I need help in fully understanding the Proof of Theorem 3.4 ...The start of Theorem 3.4 and its...

Given: U = 220 V f = 50 Hz r = 20 Ohm C = 100 μF Find: I Solution: 1) Xc = 1/(ω*C) = 1/(2*π*f*C) = 1/(2*π*50*10^-4) = 31.83 Ohm 2) R_eq - equivalent resistance R_eq = (r*Xc)/(r+Xc) = (20*31.83)/(20+31.83) = 12.28 Ohm 3) I = U/R_eq = 220/12.28 = 17.9 A True answer given in the textbook is 13 A...

This is the setup. My attempt: The ball must have the same velocity before collision as it has just after the collision as it has to return through the same path. Hence ##V_{approach} = V_{separation} \implies e = 1##. Is it correct? If not, why and how should I approach this question?

If $(x+2y)\cdot \dfrac{dy}{dx}=2x-y$ what is the value of $\dfrac{d^2y}{dx^2}$ at the point (3,0)? ok not sure of the next step but $\dfrac{dy}{dx}=\dfrac{2x-y}{x+2y}$

Excuse me, I am not too well versed in statistics. I am in engineering. Let's say I have an expected measurements(grand mean of values) and then I take another measurement of two different samples. Each sample is measured a few times to get it's own standard deviation and expected value. I...

I can show that ##\frac{d}{dt} \langle \psi (t) \vert X^2 \vert \psi (t) \rangle = \frac{1}{m} \langle \psi (t) \vert PX+XP \vert \psi (t) \rangle##. Taking another derivative with respect to time of this, I get ##\frac{d^2}{dt^2} \langle \psi (t) \vert X^2 \vert \psi (t) \rangle = \frac{i}{m...

after two simple line integrals we find that $$ f(x,y) = \arctan{p/q} + \arctan{y/x} + \pi/2$$ if ##x > 0## and $$f(x,y) = \arctan{p/q} + \arctan{y/x} - \pi/2$$ if ## x < 0 ##. And then we can just take the limits to find the value of the discontinuity (as given above). But what is the...

⟨Lx⟩=⟨l,m|Lx|l,m⟩=−iℏ⟨l,m|[Ly,Lz]|l,m⟩

By working with the following definition of minimum of a quadratic form ##r(\textbf{x})##, ##\lambda_1=\underset{||\textbf{x}||=1}{\text{min}} \ r(\textbf{x})## where ##\lambda_1## denotes the smallest eigenvalue of ##r##, how would one tackle the above problem? It is clear that the diagonal...

hi. How to obtain the expected value of x in the momentum space ?

In cosmological models the relationship between proper distance to a galaxy at the emission and absorption times can be written as ##d_p(t_e)(1 + z) = d_p(t_e)## In this case in most cosmological models we get a maximum value for the ##d_p(t_e)##. This maximum value can be also seen from the...

Note: ^ represents and. V represents or ~ represents not T represents True F represents False My solution... I started by substituting T in all variables... [p^(qVr)]^ ~r [T^(TVT)] ^ ~T (T^T) ^ F T^F F The answer is p = True q = True r = False

My brain is misfiring. I have a start value (integer) that I perform an operation on that will iteratively cause it to converge on some (unknown) integer value. I stop the iteration when the new value is the same as the old one (i.e. it has stopped changing). Until that happens, I keep...

I know nCn/2 = n!/((n/2)!)^2 = 2^(n/2)(1.3.5...n-1) but I am not getting why it's the least one.

Summary: I am not a physics student but I really need to prove that aluminium will not deform 10m underwater Hi I am doing a project of a product which will sink underwater. It will be a sealed cylindrical vessel, length 2m, width 1m, thickness 0.02m. Aluminium 6061t will be used with a yield...

In my lab report, I average the values of the index of refraction of a prism and I calculated the average uncertainty from the uncertainties in all those measurements. My questions is my final value is 1.585 +/- 0.006 I'm assuming my uncertainty should be rounded to 0.01 but does that mean my...

For a standard one-dimensional Brownian motion W(t), calculate: $$E\bigg[\Big(\frac{1}{T}\int\limits_0^TW_t\, dt\Big)^2\bigg]$$I can't figure out how the middle term simplifies. $$ \mathsf E\left(\int_0^T W_t\mathrm dt\right)^2 = \mathsf E\left[T^2W_T^2\right] - 2T\mathsf E\left[W_T\int_0^T...

Hi, Can anyone help me understand how I get to the answer on this one? The diagram shows a sketch of the graph of y = x2 + ax + b The graph crosses the x-axis at (2, 0) and (4, 0). Work out the value of b.Thank you in advance!

I'm getting 2119.36 for the concentration of mg/cubic meter of this substance...it just feels wrong though. Steps I followed: First, I figured out how many grams of the substance there were using the density formula, then saw how many were present per cubic meter after calculating the volume...

Homework Statement: This is not a homework problem. I am trying to imagine how Euler would have gone about getting the value of e, while he was trying to figure out the case of continuous compounding. Homework Equations: I know how he reached up to the equation given below. I am not sure how...

This may be a somewhat disorderly, unplanned out question, but nonetheless, I don’t know whether or not there exist any suitable academic advising websites that would be suitable for posting such. Would it be worthwhile investing time into learning theory of computation and automata via Neso...

For the following distributions find $$E[2^X]$$ and $$E[2^{-X}]$$ if finite. In each case,clearly state for what values of the parameter the expectation is finite. (a) $$X\sim Geom(p)$$ (b) $$X\sim Pois(\lambda)$$ My attempt: Using LOTUS and $$E[X]=\sum_{k=0}^{\infty}kP(X=k)=\frac{1-p}{p}$$...

Publication News article It looks increasingly like something is wrong with the older electron-based results. The story of "with electrons you measure one thing, with muons another" doesn't work any more. Is that a good thing (there might be some conclusion what the radius is in the next years)...

For question 2.2: <Ψ0|p|Ψ0> = ∫Ψ0 -iħ d/dx(Ψ0) =M Using Integration by parts i get: M = -Ψ0 iħ d/dx(Ψ0) (assuming hilbert space) Implying the expectation values for momentum are zero , however i get all the expectation values are zero for x and momentum in both states which makes no sense :(

$\tiny{219\quad inverse function}$ Let $f(x)=(2x+1)^3$ and let g be the inverse of $f$. Given that $f(0)=1$, what is the value of $g'(1)?$ $(A)\, \dfrac{2}{27} \quad (B)\, \dfrac{1}{54} \quad (C)\, \dfrac{1}{27} \quad (D)\, \dfrac{1}{6} \quad (E)\, 6$ so rewrite at...

I tried to do like this: \frac{((76 - 15)^4 + 324)((76 - 3)^4 + 324)((76 + 9)^4 + 324)((76 + 21)^4 + 324)}{((76 - 21)^4 + 324)((76 - 9)^4 + 324)((76 + 3)^4 + 324)((76 + 15)^4 + 324)} Then stucked Thanks

There are meaningful ways to assign values to things like 1 - 1 + 1 + ... or 1 - 2 + 3 - 4 + ... In a similar spirit, is it possible to assign a value to the integral of a function like this: ##f(x)=x*sin(x)## or this one: ##g(x)=Re(x^{1+5i})## (Integrals from some value, say zero, up...