Functions Definition and 1000 Threads

I have learned that they are called so because they cannot be expressed with the help of elemental methods of mathematics such as addition, subtraction, multiplication and division. But then isn't the whole of mathematics itself based on the elemental methods?

Homework Statement A player hits a volleyball when it is 4 ft above the ground with an initial vertical velocity of 20 ft/s (equation would be h = -16t2 + 20t + 4). What is the maximum height of the ball? Homework Equations quadratic formula The Attempt at a Solution t = -20 ±√202 - 4(-16)(4)...

hi! i don't quite know how to start solving for this. i understand the problem and what it's asking for but i have no idea how to start solving for it. In a volleyball game, a player from one team spikes the ball over the net when the ball is 10 feet above the court. The spike drives the ball...

Homework Statement This is from Apostol's Calculus Vol. 1. Exercise 1.15, problem 6.(c) Find all x>0 for which the integral of [t]2 dt from 0 to x = 2(x-1) Homework Equations [t] represents the greatest integer function of t. The Attempt at a Solution [/B] Integral of [t]2 dt from 0 to x...

Generating functions defined in terms of algebraic operations on real valued variables are used to enumerate answers to certain combinatorial problems. ( This morning, the exposition http://www.cs.cornell.edu/courses/cs485/2006sp/lecture%20notes/lecture11.pdf is the first of many hits on the...

Homework Statement I am working through some maths to deepen my understanding of a topic we have learned about. However I am not sure what the author has done and I have copied below the chunk I am stuck on. I would be extremely grateful if someone could just briefly explain what is going on...

Hello PF, I've got a curiosity question someone may be able to indulge me on: The set of implicit functions covers a certain function-space - the set of all functions that can be represented by an implicit relation. Parametric functions also covers a function-space, that at least overlaps...

I'm really stumped on how to do these proofs… I would really appreciate any help or insight!

Hi :o Recursion. Recursive functions. What are they used for and how they helpful?

Assign the first instance of The in movieTitle to movieResult. Sample program: #include <iostream> #include <cstring> using namespace std; int main() { char movieTitle[100] = "The Lion King"; char* movieResult = 0; <STUDENT CODE> cout << "Movie title contains The? "; if...

Find a formula for g(x)= sin(arccos(4x-1)) without using any trigonometric functions. I have the answer key right in front of me, but i still get how to start it off or the steps in solving these kind of questions or how to do it at all :/ Thanks!

Hello, I was going through the following paper: http://www.emis.de/journals/HOA/AAA/Volume2011/142128.pdf In page 6, immediately after equation (3.15), its written that "functions of the form v(t) are dense in L^2". I have been looking for proofs online which verifies the above statement but...

Hello everyone, I know that the integral of an odd function over a symmetric interval is 0, but there's something that's bothering my mind about it. Consider, for example, the following isosceles trapezoidal wave in the interval [0,L]: When expressed in Fourier series, the coefficient...

Hi I am struggling immensely with understand some aspects of chemical thermodynamics: 1) Let's say I have a solid with N atoms and am examining the ionization of individual atoms, and I am supposed to think of the electrons as ideal gasses. Or, 2) a solid or liquid is in thermal equilibrium...

Homework Statement Suppose we have the function ##f(z) = x + iy^2## and a contour given by ##z(t) = e^t + it## on ##a \le t \le b##. Find ##x(t)##, ##y(t)##, and ##f(z(t))##. Homework EquationsThe Attempt at a Solution Well, ##x(t)## and ##y(t)## are rather simple to identity. However, I am...

When you have a rational function, such as: 3x-5/x-1 After attaining things like the x and y intercepts and asymptotes, how do you know how many "pieces" of the graph there are? With linear functions/equations, you know it's a single line. Even quadratic graphs are a single piece - albeit...

1. I have to find the area between $x = 2y^2$ and $x = 1 - y$ I find the intersection points $ 1 -y = 2y^2$ $2y^2 + y - 1= 0 $ $(2y - 1)(y + 1)= 0$ so y = 1 and -1 However, x = y - 1 is not a vertical line so I am not sure how 1 and -1 can be intersections. Also, when I plug these...

I need to find the area bounded by: $y = \sqrt{x}$, $y = x/2$, and $x = 9$. I found that the intersecting point is 4 and $y = \sqrt{x}$ is the smaller function between 4 and 9 so: $$\int_{4}^{9}\frac{x}{2} - \sqrt{x} \,dx$$ and I get $$ \left[ \frac{x^2}{4} - \frac{2x^{3/2}}{3}\right]_4^9...

Hi, I have this problem to find the area between 2 curves: $y = x^2$ and $y = \frac{2}{x^2 +1}$ I found that the points of intersection are -1 and 1 and it is symmetrical. I get $2\int_{0}^{1} \ \frac{1}{x^2 + 1} - x^2 dx$which I am unable to solve. I have tried u-substitution but I end up...

Hi, I need to find the area between these 2 functions: $$y = |2x|$$ and $$y = x^2 - 3$$ So I need to find the points of intersection: $$|2x| - x^2 + 3 = 0$$ for which I get x = 3, -1 However, since there are no negative x values in y = |2x| I get $x = 3, 1$ I find that $y = |2x| $is...

I need to find the are between $$y1 = 12 - x^2$$ and $$ y2 = x^2 - 6$$. Since y1 is greater, I subtract y2 from y1 getting: $$ \int 18 - 2x^2$$ which is $$18x - 2x^3 / 3$$, The intersecting points are $$x = -3 and x= 3$$. So I find $$18x - 2x^3 / 3 from x = 3 to x = -3$$(I'm trying to...

OK, so I posted this a few days ago: https://www.physicsforums.com/threads/subtracting-the-overlap-of-functions.784184/#post-4925108 What I've come to discover is that I want to understand how I can subtract f(x) on domain [b,c] from g(x) on domain [a,d]. I want to be able to disregard both...

If $$f(z)=u(x,y)+iv(x,y)$$ is analytic in a domain D, then both u and v satisfy Laplace's equations $$\nabla^2 u=u_{xx} + u_{yy}=0$$ $$\nabla^2 v=v_{xx} + v_{yy}=0$$ and u and v are called harmonic functions. My question is whether or not this goes both ways. If you have two functions u...

I have a fun project I'm trying to do and it's been a good number of years since I did any math higher than algebra. As such, I don't know how to approach this and would like some pointers. I am trying to understand how I can subtract one function from another ONLY where the two functions...

I'm trying to derive a general work function (provided force and displacement vector-valued functions). Below are my best guesses. Can someone let me know whether these are valid? Rigid-System: ## \sum W = \int \left ( \sum \vec{F}(t)\cdot \vec{r}\,'(t) \right ) dt ## Deformable-system...

Homework Statement Solve the given initial value problem: y'' + y = u(t-\pi) - u(t-2 \pi) y(0) = 0 y'(0) = 1 Homework EquationsThe Attempt at a Solution First I took the Laplace transform of both sides: \mathcal{L}[y'' + y ] = \mathcal{L}(u(t-\pi)) - \mathcal{L}(u(t-2 \pi)) (s^{2}Y(s)...

Homework Statement Solve the given initial-value problem. y'' = 1 - u(t-1) y(0) = 0 y'(0) = 0 Homework EquationsThe Attempt at a Solution First I took the Laplace transform of both sides: \mathcal{L}(y'') = \mathcal{L}(1 - u(t-1)) s^{2}Y(s) - sy(0) - y'(0) = \mathcal{L}(1) -...

Homework Statement Let there be exactly n elements in X and exactly m elements in Y. How many different functions f: X -> Y can we form? How many different injections, surjections (and bijections for that matter)? (There is no further info on m, n.) Homework EquationsThe Attempt at a Solution...

Hello all I have a general question. When I look for a limit of a rational function, there is this rule of dividing each term by the highest power. I wanted to ask if I should divide by the highest power, or the highest power in the denominator, and why ? I have seen different answers in...

Homework Statement Suppose we have the function ##f : I \rightarrow \mathbb{C}##, where ##I## is some interval of ##\mathbb{R}## the functions can be written as ##f(t) = u_1(t) + i v(t)##. Furthermore, suppose this function is integral over the interval ##a \le t \le b##, which can be found by...

I am having trouble deciphering the opening gambit of an explanation of mean values of functions. It begins as follows: "Consider the part of the curve y = f(x) for values of x in the range a ≤ x ≤ b." A graph is shown with a curve cutting the x-axis at c with a shaded positive area bounded...

Homework Statement Let ##G##, ##H##, and ##K## be groups with homomorphisms ##\sigma_1 : K \rightarrow G## and ##\sigma_2 : K \rightarrow H##. Does there exist a homomorphism ##f: K \rightarrow G \times H## such that ##\pi_G \circ f = \sigma_1## and ##\pi_H \circ f = \sigma_2##? Is this...

This is more a conceptual question. So i am doing some self review of multi variate calculus and i am looking at functinal relations of the form F(x, y, z,...) = 0 In the book they talk about implicit differentiation. Now i fully understand how to do the mechanics of it, but i was trying to...

I've muddled my way through the majority of my weekend assignment and I'm stuck on a problem where I need to add two formulas together. 1.) 20-10cos(x*pi/4) 2.) 30+20sin(x*pi/4) I end up with a sinusoidal function which I can then graph and determine the max, min, etc. We recently went over...

Hi, so I'm having a bit of trouble understanding the normalization of radial waves. I understand that the equation is the integral of ((R^2)r^2)=1 but I'm not understanding how the process works. I need the normalization constant on R32. I got the function to come out to be...

Hi everyone, I'm having a bit of difficulty choosing an admissible function for a fixed-fixed nonuniform bar. I chose the function φ(x) = 1 - cos(2πx/L). But when solving for the the stiffness and mass coefficients: kij = ∫EA(x)φiφjdx mij = ∫ρ(x)φiφjdx, I am not sure where I should have...

I do not get what is going on here. Can someone please explain? This is sohard for me to understand. thank you

Homework Statement I have this function f(x) = \frac{6}{1+49x^2}, and i suppose to represent this function as a power series \displaystyle f(x) = \sum_{n=0}^\infty c_n x^n. Then i need to find the first few coefficients in the power series. Homework EquationsThe Attempt at a Solution After...

Hello, I want to check if f(x)=x^3 is monotonically increasing or monotonically decreasing or not monotonic at all. How do I do that, without using derivatives yet ? Thanks !

So here's the question: Suppose cos(θ) =x/4. Find expressions for the other five trigonometric functions in terms of x. In our practice problems we never had a variable x used and we were able to use the pythagorean theorem to determine the final side of the triangle and simply figure out the...

Hello! (Wave) I am looking at the proof of the following sentence: Sentence: Let $f,g$ functions. Then: $$f=g \leftrightarrow dom(f)=dom(g) \wedge (\forall x \in dom(f)) (f(x)=g(x))$$ Proof: $$\Rightarrow$$ If $f=g$, then $f \subset g$ and $g \subset f \Rightarrow dom(f) \subset dom(g)...

Hi, friends! I want to show that Hermite functions, defined by ##\varphi_n(x)=(-1)^n e^{x^2/2}\frac{d^n e^{-x^2}}{dx^n}##, ##n\in\mathbb{N}## are an orthogonal system, i.e. that, for any ##m\ne n##, ##\int_{-\infty}^\infty e^{x^2} \frac{d^m e^{-x^2}}{dx^m} \frac{d^n e^{-x^2}}{dx^n}=0 ## I have...

Hi, I have some questions regarding values of function and average acceleration/velocity and really just want to make sure i am right :) if a function, let's say acceleration = 2 m/s^2 is a constant Then the average acceleration = (v2-v1)/(t2-t1) between two points is the slope of a straight...

**Theorem:** Let $(\Omega,\mathcal{F})$ be a measurable space and let $f:\Omega \rightarrow Y$ be a given function. Let $\mathcal{A}$ be a collection of subsets of $Y$. If $f^{-1}(A) \in \mathcal{F}$ for every $A \in \mathcal{A}$, then $f^{-1}(A) \in \mathcal{F}$ for every $A \in...

Homework Statement The groups ##D_3## and ##D_4## are actually collections of functions from the sets ##\{1,2,3\}## and ##\{1,2,3,4\}##, respectively, where those integers represent the vertices of the geometric objects. Is it possible to construct a larger collection of functions from these...

Homework Statement Homework EquationsThe Attempt at a Solution http://i.imgur.com/tktQBsp.jpg [/B] I assume that you need to prove that the integral of psi1*psi0 is 0, so I have written out the integral and attempted to solve using integration by parts, but whichever way I write out the...

Consider a scenario where two individuals—Robert and Stuart—are under- taking a joint project, where the value generated from the project depends on the effort expended by both individuals. Let x be Robert’s level of effort and y the level of effort of Stuart; the value of the project for each...

Hello. In my complex analysis book I've read a theorem which says that if a sequence $$\{ f_n \}$$ of holomorphic functions on a domain $$\Omega$$ converges pointwise to a function $$f$$, then $$f $$ is holomorphic on a dense, open subset of $$\Omega$$. I know how to prove this theorem. I...

A remote control shot a single photon at a window that has a 50% chance of transmitting and 50% chance of reflecting photons. Once the photon wavepacket hits the glass (without an observer present), it propagates as a superposition of states, one in which it was transmitted and one in which it...

Homework Statement I am trying to solve the textbook questions, but the steps are not shown--any suggestions would be appreciated!: 1) Verify that x(t) = Asin (wt) + B cos(wt), where w = (k/m)1/2 is a solution to Newton's equation for a harmonic oscillator. 2) Verify that x(t) = Csin(wt +...