Inverse Definition and 1000 Threads

This is just an oddball question that's been rattling around in my head. What evidence do we have that the Coulomb force of, say, a spherical charge distribution Q, is actually nonzero at very large distances? I can easily imagine that the inverse square law is very accurate out to some...

Homework Statement Suppose that f has an inverse and f(-4)=2, f '(-4)=2/5. If G= (1/f-1) what is g '(2) ? If it helps the answer is (-5/32) Homework Equations [/B] f-1'(b)=1/(f')(a) The Attempt at a Solution Im not really sure how to start this problem. I am familiar with how to use the...

On the paper I'm reading the arctan of 35 over 65 is approx. 28.30degrees. When I use the Google calculator "arctan(35/65)" gives me 0.493941369 rad. What am I doing wrong?

How would you find the multiplicative inverse of the following? Let $R=Z_{360}[x]$ Find the multiplicative inverse of $f(x)=30x^4+120x^2+240x+7$ in $R$. Do you have to solve it using the Euclidean Algorithm? If so, I'm not sure how to do that. This problem has me stumped. Any help is much...

The closest Inverse Laplace Transform from my table is $\displaystyle \begin{align*} \mathcal{L}^{-1}\,\left\{ \frac{2\,a\,s\,\omega}{\left( s^2 + \omega ^2 - a^2 \right) ^2 + 4\,a^2\,\omega ^2 } \right\} = \sin{ \left( \omega \, t \right) } \sinh{ \left( a \, t \right) } \end{align*}$ so we...

Was just wondering is it only possible for magnetic attraction? because the force increases exponentially with decreased distance, or can it be used for repulsion. It's blatantly obvious that magnetic repulsion is a lot weaker than attraction, by a 10% margin. hence why repulsion is weaker, but...

Hello, I need to find the inverse function of the following equation y = a * ((exp(-b * x)) + (c * (1 - (exp(-b * x))))) Where a, b and c are constants. I have experimental points that fit to this equation and I want to use these values in the inverse funtion to linearize it. I have tried...

Homework Statement I have to find the inverse for this generic matrix (the dimensions are not specified, but I assume its a square matrix, I don't know if that is necessary). ##A=\left [ \begin{matrix} 1 & -1 & -1 & -1 & \dots & -1 & -1 \\ 0 & 1 & -1 & -1 & \dots & -1 & -1 \\ 0 & 0 & 1 & -1...

Homework Statement From the derivation of v(x,t) and i(x,t) I am stuck on how the inverse Fourier transform of e^(-jwx/u) was calculated. I am trying to understand how the PDE was fully solved here: http://fourier.eng.hmc.edu/e84/lectures/transmission_line/node1.htmlHomework Equations Not...

Define $f: \mathbb{Z} \to \mathbb{Z}$ via $f(n) = n^2$ for all $n \in \mathbb{Z}$. Why does $f^{-1}(\left\{0,1,2\right\}) = \left\{0,-1,1\right\}$? The definition I'm using is $f^{-1}{(T)} = \left\{a \in A: f(a) \in T \right\}$ so we have $f^{-1}({ \left\{0,1,2\right\} }) = \left\{n \in...

Homework Statement $$ \begin{bmatrix} a &b \\ c&d \end{bmatrix}$$ I'm supposed to find the inverseHomework Equations Method of Gauss-Jordan The Attempt at a Solution So I tried putting zeros in this and I got the following : $$ \begin{bmatrix} ad-ac &0 &ad &ad-a \\ 0&bc-ad &c &-a...

So, after time-independent 1D Schrodinger equation is solved, this is obtained E = n2π2ħ2/(2mL2) This means that the mass of the 'particle' is inversely related to the energy eigenvalue. Does this mean that the actual energy of the particle is inversely related to its mass? Isn't this counter...

Homework Statement If ℤ[x] denotes the commutative ring consisting of all polynomials with integer coefficients, list all the elements in ℤ[x] that have a multiplicative inverse in ℤ[x]. Homework Equations Multiplicative inverse if rs = 1 where rs ∈ R (rs are elements of the ring)...

Homework Statement Suppose R is a commutative ring with only a finite number of elements and no zero divisors. Show that R is a field. Homework Equations Unit is an element in R which has a multiplicative inverse. If s∈R with r*s = 1. A zero divisor is an element r∈R such that there exists...

I am trying to understand the following basic proposition about invertibility: a linear map is invertible if and only if it is injective and surjective. Now suppose ##T## is a linear map ##T:V\rightarrow W##. The book I read goes the following way in proving the proposition in the direction when...

Homework Statement Arbitrary derivative of inverse trigonometric function: (sin-1x) = 1/(√1 - x2) Homework Equations f-1(f(x)) = 1/f`(x) The Attempt at a Solution So basically I learned about derivatives of trigonometric functions in class, and I thought maybe this would work: deriving the...

The question: Let f: G -> H be a homomorphism of groups with ker(f) finite, the number of elements being n. Show that the inverse image is either empty or has exactly n elements. My work so far: Let h be eH (identity on H). Then the inverse image is ker(f) so has n elements, which makes it...

Help! Has anybody made a case as to why the inverse square law should apply to gravitation, a case that is based on pure reasoning, instead of empirical evidence? I have been trying to find such arguments, but no luck so far. Janein

if then to prove an inverse of this exists the following has been done to show that it is one to one what is the basis of equating the 2 square roots ?

Homework Statement Find the Laurent Series of f(z) = \frac{1}{z(z-2)^3} about the singularities z=0 and z=2 (separately). Verify z=0 is a pole of order 1, and z=2 is a pole of order 3. Find residue of f(z) at each pole. Homework Equations The solution starts by parentheses in the form (1 -...

Dear All, I'm doing some tensor calculation on the divergence of gradient (of a vector) inverse. Am I allowed to first use the nabla operator on gradient and then inverse the whole product? In other words, I'm searching for the divergence of a 2nd order tensor which is itself inverse of...

What's $1. ~ \displaystyle \arccos(\cos\frac{4\pi}{3})?$ Is this correct? The range is $[0, \pi]$ so I need to write $\cos\frac{4\pi}{3}$ as $\cos{t}$ where $t$ is in $[0, \pi]$ $\cos(\frac{4\pi}{3}) = \cos(2\pi-\frac{3\pi}{3}) = \cos(\frac{2\pi}{3}) $ so the answer is $\frac{2\pi}{3}$

I'm working through the problems in the Mooculus textbook as revision for Calculus I & there seems to be something wrong with how I'm manipulating the function to find its inverse in the following example. Homework Statement The height in meters of a person off the ground as they ride a Ferris...

Show from the definition of arctanh as the inverse function of tanh that, for $x \in (-1, 1)$ $$\tanh^{-1}{x} = \frac{1}{2}\log\left(\frac{1+x}{1-x}\right)$$ The definition of hyperbolic tangent is $\displaystyle \tanh{h} = \frac{e^x-e^{-x}}{e^{x}+e^{-x}}$ Let $\displaystyle y =...

Hi i want to find propagator of inverse harmonic oscillator to find time dependent wave function, but I can't have any ideas about this. Is it possible to help me to find it Thanks

Homework Statement Homework Equations The Attempt at a Solution Note: by real solution I mean the correct implicit derivative, not an actual real solution... Please help![/B]

Hi - my sometimes surprising set-book asks to show by series expansion, that $ \frac{1}{2}ln\frac{x+1}{x-1} =coth^{-1} (x) $ I get LHS = $ x+\frac{{x}^{3}}{3}+\frac{{x}^{5}}{5}+... $, which I think $= tanh^{-1} $ but I have found different expansions for the hyperbolic inverses, so I'd...

In 1-D the inverse of ∫ dx is dy/dx so how is the inverse of the volume integral ∫ d3x = ∫ dxdydz denoted ? Thanks

Homework Statement L-1{(2s2+3)/(s2+3s-4)2} The Attempt at a Solution I factored the denominator f(t)=(2s2+3)/((s-1)(s+4))2 now I've tried partial fractions to get (2s2+3)/((s-1)(s+4))2 = A/(s-1)2 + B(s+4)2 (2s2+3)=A(s+4)2 + B(s-1)2 by substitution, s=1 and s=-4 5=A(25) A=1/5 35=B(25)...

Homework Statement L-1{3/s1/2} Homework EquationsThe Attempt at a Solution 3L-1{1/s1/2} 3L-1{(1/sqrt(π))(sqrt(π)/(sqrt(s))} 3/(sqrt(π))L-1{(sqrt(π))/(sqrt(s))} 3/(sqrt(π))(1/(sqrt(t)) This is what I got from the solution for this problem. What tipped them off to multiply by sqrt(π)? And...

I have an exercise which says to show that for vectors, $ A \cdot A^{-1} = A^{-1} \cdot A = I $ does NOT define $ A^{-1}$ uniquely. But, let's assume there are at least 2 of $ A^{-1} = B, C$ Then $ A \cdot B = I = A \cdot C , \therefore BAB = BAC, \therefore B=C$, therefore $ A^{-1}$ is...

Homework Statement Use the convolution property to obtain the inverse Laplace transform of F(s)= e-3s * ((3s+15)/s2+25) Homework EquationsThe Attempt at a Solution = (3*(s/s2+52) + 15*(1/s2+52)) *e-3s Using table of Laplace: 3*(s/s2+52) = 3*cos(5*t) = T7 15*(1/s2+52) = 15/5*sin(5*t) =T18 e-3s...

Fourier transform is defined as $$F(jw)=\int_{-\infty}^{\infty}f(t)e^{-jwt}dt.$$ Inverse Fourier transform is defined as $$f(t)=\frac{1}{2\pi}\int_{-\infty}^{\infty}F(jw)e^{jwt}dw.$$ Let ##f(t)=e^{-at}h(t),a>0##, where ##h(t)## is heaviside function and ##a## is real constant. Fourier...

For example: If F(s) = L{t3e-16tcos(3t)sin2(t)} What would L-1{F(s)} be?

Question: A body of mass m is moving in a repulsive inverse cubed force given by F = K/r^3 where K > 0 show the path r(θ) of the body given by 1/r = A cos[β(θ-θο)] Find the values of constants A and β in terms of E, L. Work done so far: we did a similar problem with inverse square so I am...

Homework Statement [/B] I was using the Fourier transform to solve the following IVP: \frac{\partial^2 u}{\partial t \partial x} = \frac{\partial^3u}{\partial x^3} \\ u(x,0)=e^{-|x|} Homework Equations [/B] f(x) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\hat{f}(\omega)e^{i\omega...

I'm trying to show that A be a 3 x 3 upper triangular matrix with non-zero determinant . Show by explicit computation that A^{-1}(inverse of A) is also upper triangular. Simple showing is enough for me. \begin{bmatrix}\color{blue}a & \color{blue}b & \color{blue}c \\0 & \color{blue}d &...

Homework Statement If ##f(2x-1)= 6x + 15## and ##g(3x+1)=\frac{2x-1}{3x-5}##, then what is ##f^{-1}\circ g^{-1}(3)## ? a) -2 b) -3 c) -4 d) -5 e) -6 The Attempt at a Solution I think the f inverse and g inverse is ##f^{-1}(6x+15)= 2x-1## ##g^{-1}(\frac{2x-1}{3x-5})=3x+1## and,##f^{-1}\circ...

Homework Statement Hello, I have just started studying Laplace transformations and I am struggling to identify reverse Laplace transforms. I understand how to perform the transform, but going the other way is really confusing me. i.e, given ##F(P)## find ##f(t)##. If I have that ##F(P) =...

Homework Statement Show that the functions f are one-to-one and calculate the inverse function. Homework Equations f(x)= x/(1+x) (It is the equation I am having trouble with) The Attempt at a Solution I know the solution is y= x/(1-x) But no idea how to solve it. My attempt: x(1+y)=y or...

1. Homework Statement A piece of work I am doing for college (UK college that is) has me investigating the inverse square law for gamma radiation. I have collected data and the graph comes out looking right. I want to create a linearised graph of the data to investigate the results further. If...

Kindly help me find the Inverse laplace transform of the attached.

Homework Statement Hi! I have the 3x3 matrix for L below, which I calculated. But now I need to figure out how the equation below actually means! Is it just the inverse of L (L^-1)? I cannot proceed if I don't know this step. Homework Equations See image The Attempt at a Solution I put in...

Homework Statement The problem is posted below. Homework Equations In part b,I think I can use E1E2...A=I this property. But I cannot find the answer. The Attempt at a Solution By using the property,I multiply the inverse giving with σ2and σ1. However,the answer is not correct! So how to get...

I'm struggling to solve the following integral ∫ x/(√27-6x-x2) my attempt is as follows: ∫x/(√36 - (x+3)2) = ∫1/ √(36 - (x+3)2) + ∫x+1/ √(36 - (x+3)2) = arcsin (x + 3)/6 + this is where I got stuck.

Homework Statement Let v, w, ∈ V. Prove that if v + w = 0, then w = -v. V is a complex vector space.Homework Equations Axioms of a vector space. The Attempt at a Solution So, this solution was pretty easy to come up with. My question is, have I proven that w = -v or have I simply proven...

Hi, I was wondering what the major advantages and disadvantages of a pseudo inverse as compared to a regular inverse are. In class, we're usually told to the number of equations have to match the number of unknowns to find a solution. I thought that the reason for that was so we can make a...

Hey guys, So, I'm new here. And I'm of 13 years of age. I am a programmer in a platform called "ROBLOX". I wanted to create my own Animator within that platform, using Inverse Kinematics. However, searching through the web, everything is just so complicated to me. I don't seem to understand the...

find the inverse function of f(x)=ln(x-1), x>1

Homework Statement Find the Inverse laplace transform of: http://www4c.wolframalpha.com/Calculate/MSP/MSP14541hg721e74730d4fb00004644i96f59549h1d?MSPStoreType=image/gif&s=30&w=201.&h=40. Result...