Inverse Definition and 1000 Threads

Let $p(\lambda )=\lambda^3+a_2\lambda^2+a_1\lambda+a_0=(\lambda-x_1)(\lambda-x_2)(\lambda-x_3)$ be a cubic polynomial in 1 variable $\lambda$. Use the inverse function theorem to estimate the change in the roots $0<x_1<x_2<x_3$ if $a=(a_2,a_1,a_0)=(-6,11,-6)$ and $a$ changes by $\Delta...

Homework Statement B=magnetic flux density . A is the vector potential of magnetic field. How to get the formula B=∇A Homework Equations http://en.wikipedia.org/wiki/Magnetic_moment The Attempt at a Solution B=magnetic flux density . A is the vector potential of magnetic field...

Hello, The inverse square law of Newton's gravitational force, is it somehow related to each other? I mean to say P^2 is directly prop.a^3. Is it from the third law that the derivation of inverse sq.law of G=M.m/R2 is derived? Thanks.

Homework Statement Find the inverse of AB if A^(-1)= [4,0;-2,2] and B^(-1)=[-2,0;-2,3]. (See below for picture/additional information.)Homework Equations Inverse of AB = inverse of A*inverse of B The Attempt at a Solution Using above equation: (AB)^(-1) = [4,0;-2,2]*[-2,0;-2,3] =...

I am trying to solve the following problem on an old Quantum Mechanics exam as an exercise. Homework Statement Homework Equations I know that the trace of an operator is the integral of its kernel. \begin{equation} Tr[K(x,y)] = \int K(x,x) dx \end{equation} The Attempt at a...

Homework Statement compute the inverse derivative of f(x) = x^3/(x^2+1)Homework Equations n/aThe Attempt at a Solution My issue is a purely algebraic one... getting the inverse function! Attempting to solve for x yields no results! y = x^3/(x^2+1) y(x^2+1) = x^3 yx^2 + y = x^3 y = x^3 - yx^2 y...

Hi, I need to rearrange an equation: y = ax^2 + bx + c to the form of: x = ? I'm not entirely sure how to go about this and the examples I've found require the equation to be in a different form. Any tips or a point in the right direction would be great! Thanks in advance

Hi! I'm struggling with the bellow truth tables: P = I live in Paris Q = I live in France A B C P → Q Q → P ¬ Q → ¬ P S S S S S S F S F S F F F S S S F F F S S S F F F S S F S F F S F S S S Table A and C I'm...

Hi all, I have a ground excited single degree of freedom model, like that: http://www.bsw-schwingungstechnik.de/fileadmin/user_upload/images/2/graphic-passiv-isolation.jpg I know the excitation function, i.e. s(t), but I need to know the force that imposes a specific s(t). I need it...

Feynman_Lectures_on_Physics_Volume_1_Chapter_28 In 28-2 Radiation Feynman starts talking about the third term of Eq. 28.3 and why that it varies with the inverse of the distance. On page 28-4 he says that the unit vector e'r is pointed to the apparent position of the charge. I understand...

Homework Statement I have a general question about light and Lumens and the inverse square law? So Intensity = Initial Lumens/Lenth^2 So @ a Length of 1, there is no loss of light intensity. What unit is this 1. 1 meter? 1 foot? Homework Equations The Attempt at a...

inverse square vs cube = ? If the electric field falls off at the inverse square ratio, and magnetic at inverse cube, does EM radiation dissipate at 1/r^5 ratio for circularly polarized waves?

Dear all, I am reading R.A. Sharipov's Quick Introduction to Tensor Analysis, and I am stuck on the following issue, on pages 38-39. The text is freely available here: http://arxiv.org/abs/math/0403252. If my understanding is correct, then the Jacobi matrices for the direct and inverse...

\Psi=\tan^{-1}\left(\frac{\cos\omega t}{\cos(\omega t+\delta)}\right) I want to find out whether ##\Psi## increase or decrease with time t, if ##\delta## is positive and if ##\delta## is negative. \Psi=\tan^{-1}\left(\frac{\cos\omega t}{\cos(\cos\omega t \cos \delta+\sin\omega t...

Homework Statement Let A be a square matrix. a. Show that (I-A)^-1 = I + A + A^2 + A^3 if A^4 = 0. b. Show that (I-A)^-1 = I + A + A^2 + ... + A^n if A^(n+1) = 0. Homework Equations n/a The Attempt at a Solution I thought I'd want to use the fact that the multiplication of a...

I must fundamentally misunderstand what the variational method is. According to my textbook, it's used to find the minimum eigen energy of an operator (in particular, the time-independent schrodinger equation). This appears to be synonymous to finding the eigenvalues of the matrix representation...

Here is the question: Here is a link to the question: Given 0<x<orequalto 1, determine the value of inversine (x) + inversetan (squareroot(1-x^2)/x)? - Yahoo! Answers I have posted a link there to this topic so the OP may find my response.

Here is the question: Here is a link to the question: A math function question please help? - Yahoo! Answers I have posted a link there to this topic so that the OP may find my response.

Homework Statement how do I solve this question https://www.dropbox.com/s/bn958xnm5483s6u/photo%20%281%29.JPG (This link if the image is not visible : https://www.dropbox.com/s/bn958xnm5483s6u/photo%20%281%29.JPG) just so the equation is not clear it says A2 = λA - 2I The inverse should be...

This is very tricky for me. How to find the inverse laplace of 1s. I haven't been taught the integral method of inverse. Only the formula based , splitting terms kind of thing. I used MATLAB and found it was dirac delta. But how do I get to it without using the integral for inverse?

Homework Statement So I have this laplace transformation chart and was a bit unsure about the laplace and inverse laplace of this. The unit step function, where u(t) = 0 where t < 0, u(t) = 1 where t > 0. The laplace transformation chart that I have has two columns, the column on the...

Reaaly need to solve these

Homework Statement find the inverse laplace transformation of \frac{5s+4}{s^2} e^{-2s} Homework EquationsThe Attempt at a Solution I have tried to partial fractions \frac{5s+4}{s^2} and I got \frac{5}{s}+\frac{4}{s^2} and I know that the answer must have u(t-2) because of second shifting (...

Homework Statement Could anyone please check my work, The answer is wrong. Correct Answer: e^2t(-t+e^t-1) Homework Equations Inverse Laplace The Attempt at a Solution Here's my solution, please point out my mistakes. One mistake i found after taking the picture is: Its -2te^-2t ( third...

In Topology: is the multiplicative inverse of a metric, a metric? How do we define the Schwarz inequality then? if ##d(x,z) ≤ d(x,y) + d(y,z)## the inverse ##1/d(x,z)## would give the opposite?

Homework Statement see attachment Homework Equations The Attempt at a Solution I don't get the part where it says "Solving this equation for X(s), we obtain ..." Specifically jumping from 3/s(s2+3s+5) to (3/5)(1/s)-(3/5)[(s+2)/(s2+2s+5)]. How did the problem break up this...

This is problem 4.14 in Advanced Calculus of Several Variables. Two questions: Is my proof correct? And: is there a cleaner way to prove this? Show that, if ad = bc , then the matrix \left [ \begin{array}{cc} a & b \\ c & d \\ \end{array} \right] has no inverse. My attempt: Suppose there is...

If we see the form \sqrt { { a }^{ 2 }-{ x }^{ 2 } }, we always set x=asinθ How do we know that it will work in advance? Just trial & error?

Homework Statement Find the computational cost for finding the inverse of an nxn matrix via Gauss-Jordan elimination. That is setting up A|I and converting it to I|A-1.Homework Equations The Attempt at a Solution So I can't see where I went wrong, but my answer does not agree with my fellow...

Homework Statement The matrix given is row 1: [0,1] row 2: [1,0] The matrix above if you switch row 1 with row 2 is just the identity matrix. So wouldn't that matrix already be the inverse of the identity matrix? Homework Equations The Attempt at a Solution

Homework Statement Prove that the inverse of a bijective function is also bijective. Homework Equations One to One f(x_{1}) = f(x_{2}) \Leftrightarrow x_{1}=x_{2} Onto \forall y \in Y \exists x \in X \mid f:X \Rightarrow Y y = f(x) The Attempt at a Solution It...

Is this sufficient?

Homework Statement a)Use Gauss-Jordan elimination to find the inverse of A = [ 2 1 4 ] [ 1 1 2 ] [ -2 -3 -2 ] b) Use the result from part a) to find the solution of the following system. 5x+2y-3z = 5 x+y-z = -1 -3x-y+2z = 2 Homework Equations The Attempt...

Sorry for the poorly-worded title. I help tutor kids with pre-calculus, and they're working inverse functions now. They use the "horizontal line test" to see if a function will have an inverse or not by seeing visually if it's one-to-one. I was thinking about what that might imply. If a...

I'm applying laplace transform to a spring-mass system, the most basic one. I write this code which takes initial values x(0) and v(0) as input and I'm computing x(t) in matlab. But for some values it gives me complex roots for x(t) which doesn't seem possible. If not for laplace I can solve the...

Hi, I've a very trivial numerical problem where I'm currently stuck. In MATLAB the matrix Hf: >> Hf Hf = 1.0e+003 * 1.6443 1.6516 1.6583 4.8373 4.8349 4.8334 4.6385 4.6418 4.6445 -9.6014 -9.6084 -9.6154 And the following vectors which...

Homework Statement If cos^{-1}\frac{x}{a}+cos^{-1}\frac{y}{b} = \alpha then show that \frac{x^2}{a^2}-\frac{2xy}{ab}cos \alpha + \frac{y^2}{b^2} = sin^2 \alpha Homework Equations The Attempt at a Solution I assume inverse functions to be θ and β respectively. So in the second equation...

In this video: At the time 2:10, I don't understand why we have to note that \lambda^3 - 8\lambda and \lambda^2 + 1 are relatively prime. Thanks in advance

Homework Statement Solve cot^{-1} x - cot^{-1} (n^2 - x+1)=cot^-1(n-1) Homework Equations The Attempt at a Solution I can write the above equation as θ+α=β where the symbols represent the respective inverse functions. Now I take tan of both sides. Simplifying I get...

Homework Statement Let A\inM_{n}(\Re) a matrix verifying A^{3}-A^{2}-I_{n}=0 a) Show that A is inversible and calculate it b) Show that the solution X\subsetM_{n}(\Re) of the equation A^{k}(A-I_{n})X=I_{n} has a unique solution. The Attempt at a Solution I'm having...

Homework Statement What is the inverse of this logarithm equation? y=-log5(-x) i tried it and i got y=-5(-x)hm.. you know how people say that if you want to find the inverse graph of something just switch the x and y coordinates from the table of values? Well i also tried that approach and...

Hello I need some help proving the next thing, I can't seem to be able to work it out.. Let A be an nxn matrix. Prove that: (adj A)^{-1} = adj(A^{-1}) Thanks...

Homework Statement Say we have a 2D rigid body transform, with parameters p = [ p_1,p_2,p_3] for rotation, x translation and y translation respectively. I'm using the transform to .. transform an image. Is there a way to have: For a point x , y : x',y' = transform(x,y,p) <=> x,y =...

Homework Statement What is the inverse laplace transform of (1/(s+s^3))? Homework Equations The Attempt at a Solution I looked it up on wolframalpha and got 1-cos(t), but I don't understand how they got that answer. I looked up a basic laplace transform chart and didn't see anything...

Homework Statement Assume that the Derivative Rule for Inverses holds. Given that f(x) = x + f(x), and g(t) = f-1(t), which of the following is equivalent to g'(t)? a. g'(t) = 1 + t2 b. g'(t) = 1 + t4 c. g'(t) = 1 + g(x) d. g'(t) = 1 / (1 + t4) Homework Equations The Attempt at a...

Homework Statement Find inverse Laplace transform \mathcal {L}^{-1}[\frac{1}{(s^2+a^2)^2}]Homework Equations The Attempt at a Solution I try with theorem \mathcal{L}[f(t)*g(t)]=F(s)G(s) So this is some multiple of \mathcal{L}[\sin at*\sin at] So \mathcal {L}^{-1}[\frac{1}{(s^2+a^2)^2}]=\propto...

Hi I'm reading a book called Calculus lifesaver, and in the book they state that the inverse of a function f(x)= x3 is the same as f-1(x)=3√x and is the same as f-1(y)=3√y So I did a test, with a simpler function and I can't see how this is true If I have a function f(x)= 2*x Then...

Homework Statement Given f(x) = x2+3x+2, what is f-1(f(x))? Homework Equations The Attempt at a Solution Algebraically, getting f-1(x) is as follows: y=x2+3x+2 x=y2+3x+2 y=+/-√(x+0.25)-1.5 f-1(x)=+/-√(x+0.25)-1.5 f-1(f(x))=+/-√(x2+3x+2+0.25)-1.5...

Hello, let's suppose I have two functions \phi:U\rightarrow V, and T:V\rightarrow V that are both diffeomorphisms having inverse. Furthermore T is linear. I consider the function f(u) = (\phi^{-1}\circ T \circ \phi)(u), where \circ is the composition of functions. Since T is linear, we...

Homework Statement Prove that if the inverse of a function between topological spaces maps base sets to base sets, then the function is continuous. Homework Equations I have no idea. The Attempt at a Solution I seriously have no idea. This is for my analysis course, and I'm not...