Inverse Definition and 1000 Threads

I'm learning AC and theory says that the polarity of AC inverses.. even the name says 'alternating current'.. now what about the live and neutral? does the current goes from neutral to live and and vice versa? Some people says that only the phase inverses, but the current is always from live to...

Hi, this is not a homework and my problem is much bigger for me to give full details here. I came across this integral \mathcal{I}(\xi)=\int^{\xi_c}_{\xi}{\rm d}\xi^\prime\exp\left[\sqrt{2}\sigma\,{\rm Erf}^{-1}\left(1-\frac{8\pi}{3}{\xi^\prime}^3\right)\right] where Erf^{-1} is the...

Homework Statement I had a question in my midterm, it was to find inverse laplace tansform of: (4s+5) / (s^2 + 5s + 18.5) Where ^ denotes power. Homework Equations The Attempt at a Solution My answer was to find the complex roots of equation (s^2 + 5s + 18.5) , by them...

Given a trig equation, like: sin(x)² + cos(x)² = 1² or sin(x) = 1/csc(x), exist a correspondent inverse: arcsin(x) + arccos(x) = π/2 and arcsin(x) = arccsc(1/x), respectively. Thus, given an any trigonometric equation, how find its correspondent inverse?

In an AC circuit, we know that the polarity inverses, and what i know is that the flow of current also will therefore inverse.. which means that the live will become negative and the neutral will become positive.. What i can't understand is how the polarity inverses but the live is still the hot...

Why is e^-1 the inverse of natural log e? Thank you

f: (R*R)->R f(x,y)=x+y if I'm asked to write 2 right inversed fanctions of f. can I say that: f1: R-> (R*R) f1(x)= (x-1, 1) f2: R-> (R*R) f1(x)= (x-2, 2) because: f(f1(x))= f(x-1,1)=x-1+1=x well this does matches the definition of right inverse function but what bothers me I guess is...

Watching this video http://youtu.be/1JnayXHhjlg?t=5m30s, I understood the ideia the Fourier transform, that is a continuous summation of sinusoids. But now If I have amplitude and phase as function of σ and ω, the summation wouldn't be ##\sum_\sigma \sum_\omega A_{\sigma \omega} \exp(i...

f^-1 (E^c) = (f^-1(E))^c where f is map from X to Y and E is in Y. Prove equality is true.

can you check if my solution here is correct. If not can you tell me how to do it properly. thanks!

Homework Statement Problem: Given C is the graph of the equation 2radical3 * sinpi(x)/3 =y^5+5y-3 Homework Equations (1) Prove that as a set C= {(x,y) Exists at all Real Numbers Squared | 2radical3 * sinpi(x)/3 =y^5+5y-3 is the graph of a function differentiable on all real...

Homework Statement Let f be a function defined as f:(0,exp-3/2) → [-1/4, ∞), f(x) = (ln x)^2 + 3 ln x + 2 then inverse of f is equal to The Attempt at a Solution The two possibilities are exp (\dfrac{-3\pm\sqrt{4x+1}}{2}) How to decide which one is correct?

Say for some general function f(x), and g(x) = ∑x=0∞ f(x) (assuming function is defined) Is there a way to find the zeroes of g(x)? Is there any relationship between the zeroes of f(x) and g(x)? Sorry if this question is poorly asked, i just began learning about summations and infinite series...

Hi I am facing a mathematical problem in my research. I am not a maths magor and i need to do this to move on with my research. Please check the picture for the equation http://i.stack.imgur.com/jQroR.jpg Mod note: Image was too large, so deleted it, and replaced it with LaTeX. Left the...

I'm hoping that you can help me settle an argument. For a matrix \textbf{M} with elements m_{ij}, is there any sitaution where the notation (M_{ij})^{-1} could be correctly interpreted as a matrix with elements 1/m_{ij}? Personally I interpret (M_{ij})^{-1} in the usual sense of an inverse...

Homework Statement ln(sec^-1(3x^2 +1)) Homework Equations The Attempt at a Solution 1/sec-1(3x2+1) * 1/(3x2+1)(sqrt(3x2+1)2-1) * 6x Is this correct ?, do I just simplify from here ?

Homework Statement Find the inverse Laplace transform of F(s)=5e^(-8s)/(s2+36) Homework Equations The Attempt at a Solution I know that to find the inverse Laplace transform of this function, I start by factoring out (e^(-8s)) to end up with 5/(s^2+36), and that my final answer...

Obtaining the Equation of a Path I'm working on a project for myself in SolidWorks which involves a scissor-type mechanism. The bottom ends of the linkages are attached to disks that are free to rotate around the central hub where all the gears are attached. On the other side of the hub is...

is it true that \frac{1}{g_{ab}}=g^{ba}? I am a bit confused by the index notation. I especially wonder about the inversion of the indices. Could somebody clarify this please?

Homework Statement Take the inverse Fourier Transform of 5[\delta(f+100)+\delta(f-100)]\bigg(\frac{180+j2\pi f*0.0135}{1680+j2\pi f*0.0135}\bigg)Homework Equations g(t)=\int_{-\infty}^{\infty} G(f)e^{j2\pi ft}dt The Attempt at a Solution g(t)=\int_{-\infty}^{\infty}...

an S-shaped lawn sprinkler (an S-shaped pipe on a pivot) in which water squirts out at right angles to the axis and makes it spin in a certain direction is taken and if you had a lake, or swimming pool (a big supply of water) and you put the sprinkler completely under water, and sucked the water...

Homework Statement The intensity (I) of sunlight (the received power per unit area) drops with distance (d) from the sun according to the inverse square law - i.e I2/I1 is proportional to (d1/d2)^2 What is the total power received at Earth (above the atmosphere) per unit of surface area...

Digging in the wiki, I found this relation between 'arc-functions' and 'arc-functions-hyperbolics" \\ arcsinh(x)= i \arcsin(-ix) \\ arccosh(x)= i \arccos(+ix) \\ arctanh(x)= i \arctan(-ix) https://it.wikipedia.org/wiki/Funzioni_iperboliche#Funzioni_iperboliche_di_argomento_complesso...

Homework Statement I have to find ##\tan^{-1}(2i)##. Homework Equations The Attempt at a Solution So far I have ##\tan^{-1}(2i)=z\iff tan z= 2i\iff \dfrac{sin z}{cos z}=2i ##. From here I get that ##-3=e^{-2zi}##. I do no know how to take it further to get ##z=i\dfrac{\ln...

A family of functions is a set of functions that share one or more properties. ie: The family of quadratics with zeros 1 and 10, or the linear functions with a slope of 20. there is a family of linear functions where each member is its own inverse. What linear property defines the family? (I...

The function y = x is its own inverse. Why?

I found this forum on Google. This may not be the right section so excuse me if so. I have a rather simple question though. When you take a magnifying glass on a sunny day and position it just right over a piece of paper, the paper will start to burn. Is the inverse square law (distance) the...

Trying to see the logic in deriving length contraction and time dilation using the Lorentz transformations and inverse Lorentz transformations. In the following treatise it leads to ambiguities. Given ##Δ\acute{t}=\gamma(Δt-\beta c^{-1}Δx)## (1) ##Δ\acute{x}=\gamma(Δx-\beta c Δt)##...

1. Given: The DTFT over the interval |ω|≤\pi, X\left ( e^{jω}\right )= cos\left ( \frac{ω}{2}\right ) Find: x(n) 2. Necessary Equations: IDTFT synthesis equation: x(n)=\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}X\left ( e^{jω} \right ) e^{j\omega n}d\omega Euler's Identity...

If given an one-form like: ##\omega = u dx + v dy##, dω is ##d\omega = \left ( \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y}\right )dxdy##. So, is possible to make the inverse path? Given: ##d\omega = Kdxdy## , which is the expression for ω ? ##\omega = ? dx + ?dy##

Homework Statement Find the inverse Fourier transform of f(w)=1 Hint: Denote by f(x) the inverse Fourier transform of 1 and consider convolution of f with an arbitrary function. Homework Equations From my textbook the inverse Fourier transform of f(w)=\int F(w)e^-iwt dw The...

Hi there, Let S denote the shift operator on the Hardy space on the unit disc H^2, that is (Sf)(z)=zf(z). My question is to show the following identity (1-\lambda S^*)^{-1}S^*f (z)=\frac{f(z)-f(\lambda)}{z-\lambda}, where \lambda,z\in\mathbb{D} Thanks in advance

With a Laplace transform, we can remember common set ups; for example, \[ \mathcal{L}\{e^{-at}\} = \frac{1}{s + a}. \] When it comes to the inverse Laplace transform, I can only find the tables to remember in a book. However, if we go back to the Laplace transform, we can always do \[...

I am having difficulty understanding the following problem. I feel it should be very simple but am unsure how to interpret it. A relation ##R## is defined on ##N## by ##aRb## if ##\frac{a}{b} \in N##. For ##c, d \in N##, under what conditions is ##c R^{-1} d##? (Exercise 8.6 from Chartrand...

Please see attached. I am not sure whether my example of this function is correct. f(x) = ##sin(\frac{\pi x}{2})## obviously, f(x) is continuous on [-1,1] and differentiable on (-1,1) Inverse of f(x) will be ##\frac{2 sin^{-1}x}{\pi} ## and d/dx (inverse of f(x)) will be ##\frac{2}{π...

Homework Statement Doing some exam revision and one of the questions from an old exam has me stuck at the last step, simply need to inverse the following F( \omega ) = \frac{e^{i \omega}}{1+\omega ^2} We're allowed to use a table on the exams but I cannot find anything quite...

Say we want to differentiate \arcsin x. To do this we put y=\arcsin x. Then x=\sin y \implies \frac{dx}{dy}= \cos y. Then we use the relation \sin^2 y + \cos^2 y = 1 \implies \cos y = \sqrt{1 - \sin^2 y} = \sqrt{1 - x^2}. Therefore \frac{dy}{dx} = \frac{1}{\sqrt{1 - x^2}}. My question is that...

I can derivate x(y) wrt y using the derivative of y(x) wrt x, follows the formula: \frac{dx}{dy}=\frac{1}{\frac{dy}{dx}} until same the 2nd derivative (taking the 2nd diff form of x and deriving wrt to x):d^2x=\frac{d^2 x}{dy^2} dy^2 + \frac{dx}{dy} d^2y \frac{d^2x}{dx^2}=\frac{d^2 x}{dy^2}...

So, I'm doing a problem where I take arctanh to a limit, and I was wondering if the arctanh function goes to infinity if the argument inside of the function goes to infinity when passing through the limit.

Prove that if operator on a hilbert space $T$ commutes with an operator $S$ and $T$ is invertible, then $T^{-1}$ commutes with $S$. $T^{-1}S$=$T^{-1}T^{-1}TS$=$T^{-1}T^{-1}ST$

Let $T_{n}$ be a sequence of invertible bounded linear operators with limit $T$ Prove that $(T_{n})^{-1}$ tends to $T^{-1}$

Homework Statement d/dθ csc-1(1/2)^θ = ? Homework Equations d/dx csc-1(x) The Attempt at a Solution I don't know how to deal with the exponent θ

When I place the trigonometric functions in the "wolfram google", it informs the parity of the function, so, sin(x), sinh(x) -> odd cos(x), cosh(x) -> even tan(x), tanh(x) -> odd cot(x), coth(x) -> odd sec(x), sech(x) -> even csc(x), csch(x) -> odd arcsin(x), arcsinh(x) -> odd...

Homework Statement Prove/Disprove following function being one-to-one.If yes,find its inverse. g(x)=x-\frac{1}{x},x>0 Homework Equations The Attempt at a Solution My tutor said that it is one-to-one,but I found that the are two solutions for g-1(x). Are there any mistakes...

Hi, I would like to find the inverse Laplace transform for 11/(s^2+16)^2 I have tried to expand it using the following partial fraction decomp to find the constants and take the inverse Laplace but this did not work C1(s)+ C2/(s^2+16) + C3(s)+C4/(s^2+16)^2 Does anyone have any suggestions?

Homework Statement Find: Inverse Laplace for x(t)= (e)^-5t*(t)^4 using laplace table and laplace properties. Homework Equations The Attempt at a Solution Well, I have been working on this problem for a few days now and cannot seem to figure it out. The two functions are not...

Homework Statement For a group G consider the map i:G\rightarrow G , i(g)=g^{-1} For a subgroup H\subset G show that i(gH)=Hg^{-1} and i(Hg)=g^{-1}H Homework Equations The Attempt at a Solution I know that for g_1,g_2 \in G we have i(g_1g_2)=(g_1g_2)^{-1}=g_2^{-1}g_1^{-1} Then...

Homework Statement If * is a binary operation on a set B, and the domain of definition is B^2, if * is associative and the neutral element is p. If r and l are elements of b we can say that r is a left inverse of l under * iff r * l = p, and l is a right inverse of r iff l * r = p. Show that if...

Find the mean square error using the pseudo inverse approach. I am given a 11X9 matrix A, a 11X1 vector F and R = 11X11 diagonal matrix so Rhat = A[(A'A)^-1 ]A' R . Then I get a 11X11 matrix. Shouldn't I get getting a 8X11 matrix How do I get the most optimum vector F?

This is for Calculus II. I've found most of the integrations on inverse trig functions to be pretty simple, but for some reason this one is throwing me off. Homework Statement \int\frac{x+5}{\sqrt{9-(x-3)^2}}dx The Attempt at a Solution I started by breaking the integral up...