Functions Definition and 1000 Threads

This was the question, The above solution is the one that I got originally by the question setters, Below are my attempts (I don't know why is the size of image automatically reduced but hope that its clear enough to understand), As you can see that both these methods give different answers...

I would like to know if any of you think there's any sort of connection, analogy, or common features between, sets in set theory and wave functions in QT? Wave functions lack trajectories, so do sets. Wave functions also distribute over areas, as sets can do. To my understanding, wave...

State the domain and range for one cycle of y=cos(3(x - 45°)) +2 Show your work.

Find the first two positive x-intercepts for y= -2cos(3(x-25°)) +1 (Can someone help me for this)

Sinusoidal Functions... Can someone help me with this. Describe the transformations that are applied to y= -4cos[2(x-30°)] +5 (State any shifts, stretches, compressions, or reflections).

Sometimes, when I code something, I am naming the local variables in the function same as the global variable. Such as, my_var = 13 def iseven(my_var): if my_var % 2 == 0: return True return False print(iseven(my_var)) As you can see my_var is defined globally but also used...

I would like to ask whether if operators ##A## and ##B## commute also operators ##e^A## and ##e^B## commute? Also I have a question is it possible that ##e^A## is matrix where all elements are ##\infty## so that ##e^A \cdot e^B-e^B\cdot e^A## has all elements that are ##\infty##?

The following parametrizations assume a counter-clockwise orientation for the unit square; the bounds are ##0\leq t\leq 1##. Hypotenuse ##(C_1)## %%% ##r(t)=(1-t,1-t)## ##dr=(-1,-1)\,dt## ##f(r(t))=f(1-t,1-t)=(a(1-t)^2,b(1-t)^2)## ##f\cdot dr=-(a+b)(1-t^2)\,dt## \begin{align} \int_{C_1} f\cdot...

DIS observables can be expressed in terms of structure functions F1, F2 and FL. There exists the relation ##F_L = F_2 - 2xF_1##. We can write $$ F_L = \sum_a x \int_x^1 \frac{dy}{y} C_{a,L}(y,Q) f_a (\frac{x}{y},Q) $$ and similarly for ##F_1## and ##F_2##: $$ F_1 = \sum_a x \int_x^1...

"Consider a string of length L that is connected at both ends to supports and is subjected to a load (external force per unit length) of f(x). Find the displcament u" https://i.stack.imgur.com/yVIDG.png We need to solve this: $$Tu_{xx} = f(x)$$ subject to $$u(0)=u(L)=0$$ But i don't understand...

g(f(x))=\( g(f(x))=2/(1/x-4)+4 \)

Hello everyone first time here. don't know if it's the correct group... Am having some issues wiz my maths homework that going to count as a final assessment. Really Really need help. The function (f), with a period of 2π is : f(x) = cosh(x-2π) if x [π;3π].. I had to do a graph as the first...

Hi everyone! =) . I'm having some issues with this exercises, It's about functions. I remember the basic geometrics formulas and how to get the area and perimeter of a square or a circle but I don't get it. I need an explanation. 1. Express the area A of a square as a function of (a) the length...

Problem: Find the cardinality of the set ## A = \{f \in \Bbb N \to \Bbb N. \forall n\leq m .f(n) \geq f (m) \} ##. I know that ## A \subseteq P(\Bbb N \times \Bbb N) ## implies ## |A| \leq |P(\Bbb N \times \Bbb N)| = | P(\Bbb N) | = \aleph ##. So I have a feeling that ## \aleph \leq |A| ##...

What branch of mathematics studies multinomial functions of matrices? ( i.e matrix valued functions of square matrices such as ##f(A,B,C) = ABC + BAC + 2A^2 + 3C##)

1) -|2x-3|+|5-x|+|x-10|=|3-x| 2) |2x-3|-|5-x|-|x-10|-|3-x|=28 3) -|2x-3|+|5-x|+|x-10|≥|3-x| How can we solve these problems? The method I know is to plug in the critical values to see which modulus becomes positive and which one becomes negative. Then find out the values of x for which the...

Hey :) Firstly I want to thank everyone who takes their time to read through this post and who tries to help me. So the issue is the following: I wrote a python code that creates a Lindbladian, and I wanted to try to calculate the Greens function using the Lehmann representation. For the...

I found the following functions ( In lambda notation ) to be injective, and now I am trying to find the inverse functions for them ( the inverse for the Image of ## f ## ) but I am stuck and I need help: 1. ## f = \lambda n \in \mathbb{N}. (-1)^n + n^2 ## 2. ## f = \lambda g \in \mathbb{R}...

Suppose ##f## is not uniformly-continuous. Then there is ##\epsilon>0## such that for any ##\delta>0##, there is ##x,y\in K## such that if ##|x-y|<\delta##, ##|f(x)-f(y)|\geq \epsilon##. Choose ##\delta=1##. Then there is a pair of real numbers which we will denote as ##x_1,y_1## such that if...

My attempt involved using the big-Oh notation, I think this should work but I am not sure how to go about it. The two functions are g(n) = 6^n/n^5 and h(n) = (ln n)^84. I thought that I could use the inequality 6^n < ln(n)^84 and 6^n/|n^5| = |g(n)| < 6^n and put those inequalities together...

Here is the example and solution in full. I have circled where I'm at and highlighted the part that's tripping me up. I managed to get... and getting everything in terms of the angular frequency seems to be critical for getting the plots for the Frequency Response. I checked my notes on RC...

Hi, 2 part question trying to get tetrahedron Finite Element shape functions working: 1) How do I properly setup the shape coefficient matrix and 2) How do I build the coefficient quantities in the shape functions properly? ANY tips or corrections may unblock me and would be of much value...

I understand that on Riemannian manifolds, the transition functions that glue charts together are coordinate transformations (Jacobian matrices). However, I am not quite sure how transition functions work in the context of Lie groups and Fiber bundles. Do we consider the manifolds to be flat...

I want to check my calculations via mathematica. In the book I am reading there's this expansion: $$\frac{(1+\frac{1}{j})^x}{1+x/j}=1+\frac{x(x-1)}{2j^2}+\mathcal{O}(1/j^3)$$ though I get instead of the term ##\frac{x(x-1)}{2j^2}## in the rhs the term: ##-\frac{x(x+1)}{2j^2}##. So I want to...

Problem: Find the set of all harmonic functions ##u(x,y,z)## that satisfy the following inequality in all of ##R^3## $$|u(x,y,z)|\leq A+A(x^2+y^2+z^2)$$ where ##A## is a nonzero constant. Work: I removed the absolute value bars by re-writing the expression $$-C-C(x^2+y^2+z^2)\leq u\leq...

We need to show that ##\lim_{x \rightarrow a}f(x)=f(a), \forall a \in \mathbb{R}## . At first, I tried to show that f is continuous at 0 and from there I would show for all a∈R. But now, I think this may not even be true. I only got that f(0)=0. I'm very confused, I appreciate any help!

Here is the problem (8b). I was asked to write out why the circled part was true. I know that since the function is concave down then f"(x)<0. That is a fact. What I am having trouble with is why they can say the next part. What I thought was L(x) is the tangent line and all tangent lines...

My understanding of the n-correlation function is \begin{equation*} \langle \phi(x_1) \phi(x_2) ... \phi(x_n)\rangle = i \Delta_F (x_1-x_2-...-x_n) \end{equation*} Where ##\Delta_F## is known as the Feynman propagator (in Mathematics is better known as Green's function). Let us analyze...

Hello. Sin and cos separately oscillates between [-1,1] so the limit of each as x approach infinity does not exist. But can a quotient of the two acutally approach a certain value? lim x→∞ sin(ln(x))/cos(√x) has to be rewritten if L'hôp. is to be applied but i can't seem to find a way to...

Hi PF! Do you know of any examples of the Ritz method which use Bessel functions as trial functions? I’ve seen examples with polynomials, Legendre polynomials, Fourier modes. However, all of these are orthogonal with weight 1. Bessel functions are different in this way. Any advice on an...

R is the region bounded by the functions f(x)=3√x−4 and g(x)=3x/5−8/5. Find the area A of R. Enter answer using exact values.

Simplify $\left(\tan \dfrac{2\pi}{7}-4\sin \dfrac{\pi}{7}\right)\left(\tan \dfrac{3\pi}{7}-4\sin \dfrac{2\pi}{7}\right)\left(\tan \dfrac{6\pi}{7}-4\sin \dfrac{3\pi}{7}\right)$.

Let $$ \mid h \mid $$< 1. Which of the following functions are O(h)? Explain. $$ -4h $$ $$h+h^2 $$ $$ \mid h \mid ^{0.5} $$ $$h + cos (h) $$ Based on my notes, f(h) = O(h) only if $$ \mid f \mid $$ ≤ C $$ \mid h \mid $$, where C is a constant independent of h. I can only solve for the...

Hi, I have a question about probability transformations when the transformation function is a many-to-one function over the defined domain. Question: How do we transform the variables when the transformation function is not a one-to-one function over the domain defined? If we have ## p(x) =...

What are the units of the trigonometric functions sinus, cosinus etc? If I take say Sin(0.5), what would the units of the output be?

I am trying to plot two functions a(t) and b(t) that both use a common intermediate result K. In my actual code K would be a slow-ish calculation. To reuse the K across a and b, I am putting them into a single module that provides an array {a, b} to the Plot[] function. (BTW, the Evaluate[] is...

I plotted the x(red dots) coordinates and y coordinates( black dots) of extremums of functions x^x^a (the x coordinate of the dots is a and y coordinate of the dots is x or y coordinate of the extremum). Is there a function, on which are located all the black dots or all the red dots? P.S. The...

I want to plot the ratio f1(x) / f2(x), where they have some common zeros. Does Mathematica have a feature that will do this, switching automatically to f1'(x) / f2'(x) when appropriate, avoiding F.P. errors and optimizing numerical precision? If not, is there a good way to implement this?

I am using square roots, however, I am confused over how many significant figures (s.f.) to keep. Suppose I have ##\sqrt{3.0}##, which has 2 s.f. From three different sources, I'll put a summary in brackets: https://www.kpu.ca/sites/default/files/downloads/signfig.pdf (if 2 s.f. in the data...

Problem: Show that the set of differentiable real-valued functions ##f## on the interval ##(-4,4)## such that ##f'(-1) = 3f(2)## is a subspace of ##\mathbb{R}^{(-4,4)}## This is my first bouts with rigorous mathematics and my brain is not at all wired for attacking problems like this (yet). I...

Summary:: Problem interpreting a vector space of functions f such that f: S={1} -> R Hello, Another question related to Jim Hefferon' Linear Algebra free book. Before explaining what I don't understand, here is the problem : I have trouble understanding how the dimension of resulting space...

Hello! (Wave) I want to solve the recurrence relation $$T(n)=4T{\left( \frac{n}{3} \right)}+n \log{n}.$$ I thought to use the Master Theorem. We have $a=4, b=3, f(n)=n \log{n}$. $\log_b{a}=\log_3{4}$ $n^{\log_b{a}}=n^{\log_3{4}}$ How can we find a relation between $n^{\log_{3}{4}}$ and...

Is there a name for functions that are linearly dependent with its derivatives? i.e. a function ##f(x)## such that, for some value of ##n## it fulfills $$f^{(n+1)} = \sum_{k=0}^{n} \alpha_k f^{(k)}$$ are linearly dependent?

Hello, I am doing a vector space exercise involving functions using the free linear algebra book from Jim Hefferon (available for free at http://joshua.smcvt.edu/linearalgebra/book.pdf) and I have trouble with the author's solution for problem II.1.24 (a) of page 117, which goes like this ...

Which of the following are true? Select all options. Assume that f:A→B and g:B→C. If f and g are injective, then so is g∘f If f and g are surjective, then so is g∘f If f and g are bijective, then so is g∘f If g∘f is bijective, then so are both f and g If g∘f is...

So I attempted this problem and to satisfy the first condition (for t in the range of [1, 5]), I drew the straight line that has a slope of 5 (i.e. f(x)=5x). I just don't understand how I can have the same function with a different slope (average rate of change) for the interval [1,10] or for [2...

I saw this statement from the textbook "Quantum physics of atoms, molecules, solids, nuclei, and particles" second edition pg 166. According to the text, is the author saying the solution to the TISE is the eigenfunction and when you multiply the time dependent part, you get the wave function? I...

I saw something in my notes that I didn't understand... we have ##y=f(x)##, and consider an implicit equation of the form ##g(y) = f(x)##. They then say that ##f=g##. Why is that true? I would have thought$$f = \{ (a,f(a)) : a\in \mathbb{R} \} \subseteq \mathbb{R}^2$$whilst ##g## is just$$g = \{...

In classical mechanics, we have either Newton’s laws or a Lagrangian in terms of coordinates and their derivatives (or momenta) and we can solve them for the behavior of the system in terms of these variables, which are what we observe (measure). In QM, we quantize classical mechanics by making...

Create one equation of a reciprocal trigonometric function that has the following: Domain: ##x\neq \frac{5\pi}{6}+\frac{\pi}{3}n## Range: ##y\le1## or ##y\ge9## I think the solution has to be in the form of ##y=4sec( )+5## OR ##y=4csc( )+5##, but I am not sure on what to include...