Function Definition and 1000 Threads

Could someone confirm my answer please?

The question arose when watching Sean Carroll video: The Biggest Ideas in the Universe _ Q&A 6 - Spacetime 3:50 - 13:30 Because photons follow null geodesic in spacetime the question arose from viewers: "photons do they really experience no time this is a question" And in the answer: "but if...

Hello fellow physicists, I need to calculate the rotational partition function for a CO2 molecule. I'm running into problems because I've found examples were they say this rotational partition function is: ##\zeta^r= \frac T {\sigma \theta_r} = \frac {2IkT} {\sigma \hbar^3}## Where...

Here's my attempt: I would like to confirm my answers.

Since the index of the root is odd, the domain is going to be ##R##, and I can calculate the second derivative to be: $$y''=\frac{1}{3}\times \frac{e^x(e^x-3)}{3(e^x-1)^{\frac{5}{3}}}$$ Studying the sign of this function, it results positive for ##x<0 \vee x>ln(3)##, so the main function will be...

I have the solution to the problem, and I mechanically, but not theoretically (basically, why do the C(s) and R(s) disappear?), understand how we go from ##(s^5 + 3s^4 + 2s^3 + 4s^2 + 5s + 2) C(s) = (s^4 + 2s^3 + 5s^2 + s + 1) R(s)## to ##c^{(5)}(t) + 3c^{(4)}(t) + 2c^{(3)}(t) + 4c^{(2)}(t) +...

is it correct that the continuum states will be free particle states? and the probability will be |< Ψf | ΨB>|^2 . Where Ψf is the wave function for free particle and ΨB is the wave function for the bound state when the depth is B.

Hi, I'm reading the following paper (L. Chua) about the state-of-art of dynamic non linear circuit analysis -- Chua_Dynamic_Circuits I've a doubt about Theorem 2 on section 3.2 On the Existence of the Resistor Function that establishes sufficient conditions for the existence of network...

I have the above transfer function for this filter design The transfer function becomes which then becomes Now when I try to use this transfer function to plot a bode plot, I always end up with negative terms which i can't get the square root of For example, at 1hz, where w = 6.283 R1 = 1705...

the solution

Given the equation : ##|y| x = x##. Two conditions are possible : (1) ##\underline{y\geq 0}## : ##xy = x\Rightarrow \boxed{y = 1}\; (x \neq 0)##. We note that except for zero, ##-\infty<x<+\infty## for this case. (2) ##\underline{y < 0}## : ##-xy = x\Rightarrow \boxed{y = -1}\; (x \neq 0)##...

it really took me time to figure out as to how that equation in aterisk was arrived at...i just noted that both sides of the equation were multiplied by ##-\frac {1}{3}## any particular reason for that? what is the common thinking around that? can one multiply both sides by say ##\frac {1}{6}##...

Hi, I have this scheme, in which there are 3 segments: - I is coaxial to c axis and free to rotate in the origin. Length d1 - II is coaxial with a axis and free to rotate around c axis. There a fixed angle θ between a and c axis. Length d2 - III is welded to II, it's the PM segment. α is fixed...

Let's take an example - f: N-->N f(x)= 2x This is called the Rule of the Function. The rule of the function tells us the relationship between the elements (x,f(x))of the ordered pairs in the Function Set. So, if the...

Considering the measure of angles in radians, that are real numbers, the concept of of trigonometric function spreads to all real numbers. Any real number can be considered as an angle of the first circumference and a ##\mathbb{K}## number of circumferences. We can consider the function...

$\tiny{gre.al.12}$ The graph of $y=\left|x-6\right|$ is is the standard $(x,y)$ coordinate plane. Which of the following transformations. when applied to the graph of $y=\left|x\right|$, in the graph of $y=\left|x-6\right|$? a. Translation to the right 6 coordinate units b. Translation to...

When studying classical mechanics we are told that light is the propogation of electromagnetic waves. This makes perfect sense, as I can imagine these fields behaving this way, and in turn have an associated wave length. When learning about QM, I have heard that the wavelength of a (any)...

I have a project folder called Projects and inside that folder I have a file called my_functions.py. Now I have a folder named Project 1 and inside there is another python file called test.pySo it is something like -Projects- my_functions.py -Project 1- test.py Now I...

I calculated the derivative of this function as: $$\frac{6x^3-4x}{3\sqrt[3]{(x^3-x)^2}}$$ Now, in order to find and later study non-differentiable points, I must find the values which make the argument of the root equal to zero: $$x^3-x=0 \rightarrow x=0 \vee x=\pm 1$$ and then find the left and...

I am struggling to understand Callen's explanation for stability, I understand that the concavity of S(U) must be negative because otherwise we can show that this means that the temperature increases as the internal energy decreases (dT/dU<0) but I cannot understand equation (8.1) which...

In the notation of Function ---> f(x)=y Here f represents the function and x is the variable in the function. we read f(x) as "f of x"or "function of the variable x" what does "function of x " mean that we read ? in this notation what does round brackets ()...

Hi! I have a question about integrating Planck's function of blackbody radiation. Why is it that the area under the blackbody curve will be less than the spectral radiance of individual wavelengths? For example, integrating the Sun's curve over all wavelengths yields a smaller value than the...

The exact value of \int_{-1}^1 \arcsin (x) \arccos (x) \arctan(x) \mathrm{d} x.

I have to find: g(1)= and g(5)= I have drawn the graph and I am a little unsure where to go from there. I know area is involved somehow but not entirely sure what to do. Any help is appreciated

I try to proof it but i got stuck right here, i want your opinions Can I get a solution if i continue by this way? or Do I have to take another? and if it is so, what would yo do?

Where does the volume even come from? Any help would be appreciated!

Let a continuous function f: R -> R such that f(x)f(f(x)) = 1 and f(2020) = 2019. What is the value of f(2018)? I am having problem with this question. I already tried, through various attempts, to find the function explicitly which satisfy this condition and f(0) different of 0. But it leads...

Hi all Physics Forum User, I am again coming to you to ask for help. For the above question I can't make sense of how a larger G will cause Vo/Vi to approach 1. For this I'll call Vo=V and Vi=I As can be seen from the control loop B = A*H and V = B*K hence V = A*H*K Also A = I - C and...

I often encounter functions called "polynomial" in numerous fields. I don't see an obvious common trait other than that they're usually describing a real-valued continuous function. What aspects are typical or universal or distinct? What structures can be polynomial? Some sources say that...

Find a polynomial of degree 3 with real coefficients such that each of its roots is equal to the square of one root of the polynomial $P(x)=x^3+9x^2+9x+9$.

I must find the Lagrangian for an undamped pendulum using the diagram showed below, I've no idea what to do with the second angle φ2 because is measured from the line that joins the two pivot points. The ecuations I must obtain are as follows I get so many different things but I can't reach...

Hi everyone, I have to solve this homework without having any books where to find the theroical topic or examples, so if you could help me find materials that I can use to understand or you want to try help me understand how to get the solution would be very helpfull. I don't have enough time to...

First, I calculated the derivative of $$D(\sqrt{ax})=\frac{a}{2\sqrt{ax}}$$ Then, by applying the due theorems, I calculated the deriv of the whole function as follows: $$ f'(x)=\frac{\frac{a}{2\sqrt{ax}}(\sqrt{ax}-1)-\sqrt{ax}(\frac{a}{2\sqrt{ax}})}{(\sqrt{ax}-1)^2}=...

I tried parametrizing the domain using spherical coordinates, with theta and phi. I also tried the method of lagrange multipliers, but the substitutions don't easily result in an easy solution. It requires solving five equations for five variables, and no easy way to isolate variables. I think...

We have the function d from VxV to another set(not necessarily R) for which the following properties are to be satisfied: i) d(x,y)=0<=>x=y ii)d(x,y)=d(y,x) iii)d(x,z)≤(d2(x,y)+d2(y,z))1/2 ∀ x,y,z ∈ V. What do you say? Would this function have interesting properties on a set and theorems to be...

Good day as said in the title i need the domain of definition of of the function f(x,y)=x^y for me as x^y=expontial (y*ln(x)) so x>0 but the solution said more than that I really don't understand why we consider the case (0,y) in which while should be different from 0, because I will never...

Is the partition function used in number theory and statistical mechanics the same thing?

Which of the following statements is equivalent to saying that a function f:A→B is onto? There are 8 options, select all that are correct. x f(A)=B x In the arrow diagram representing f, every point in B has an arrow pointing at it. x ∀y∈B ∃x∈A such that f(x)=y x f−1(B)=A...

Is the main function really a function, or it is just the name we give to functions like "def Anyfunction: "? I searched about this "main function" and it always appears with the def command. So i am not sure what is the difference between both, if there is.

What is the relation between Wannier function and LCAO in tight-binding (TB) model? I know in TB we use LCAO but why we have an alternative approch using Wannier function? For example as said in this lecture note: But I don't understand why we use wannier function? Or in general why we use a...

\lim_{x\to0}\frac{sin2x+sin6x+sin10x-sin18x}{3sinx-sin3x=} A. 0 B. 45 C. 54 D. 192 E. 212 Either substituting or using L'Hopital gives \frac00. Is there any way to simplify it and make the result a real number?

Hi experts, I am a student of electronics engineering and a new member. I have few questions related to Oscilloscope, function generator and Digital Multimeter. 1. what does the DC offset on the function generator do? 2. What is the frequency range and type of signals available? 3. What is the...

There are many representations of the delta function. Is there a place/reference that lists AND proves them? I am interested in proofs that would satisfy a physicist not a mathematician.

I had found the singuarity function for the shear and moment. I have a hard time calculating the singuarity function and graphing it using excel. Can anyone explain how to calculate singuarity function and graphing it using excel? Many thanks for your help

In this code, I define a function of x as the sum of the first x integers. In[7]:= fnSum[x_] := Sum[k, {k, 1, x}] In[8]:= fnSum[x] Out[8]= 1/2 x (1 + x) In[9]:= fnSum[3.5] Out[9]= 6 I would like now to take the symbolic formula underlying fnSum, and use it with real arguments. How can I...

I was wondering if it's possible to plot a wave function that is a function of 3 coordinates, such as (x, y, z). The text my class uses calls this Quantum Mechanics in 3 dimensions, but wouldn't this technically by four dimensions?

Hi, I am wondering if it is possible to demonstrate that: tends to in the limit of both x and y going to infinity. In this case, it is needed to introduce a measure of the error of the approximation, as the integral of the difference between the two functions? Can this be viewed as a norm...

I'll write my procedure: $$\lim_{x\to\infty}[\frac{(a-2)x^3+x^2}{ax^2+6x+1}]\rightarrow\frac{x(a-2)}{a}\in \mathbb{R}$$ And now, assumed that everything's correct, how do I assign ##a## a value for having that limit finite and ##\in \mathbb{R}##, and so an horizontal asymptote?

Let $a,\,b$ and $c$ be real numbers such that $\sin a+\sin b+\sin c\ge \dfrac{3}{2}$. Prove that $\sin \left(a-\dfrac{\pi}{6}\right)+\sin \left(b-\dfrac{\pi}{6}\right)+\sin \left(c-\dfrac{\pi}{6}\right)\ge 0$.