Inverse Definition and 1000 Threads

Homework Statement I have this lowpass circuit which I have transformed to the S-domain. The circuit is to be exposed to a unit step, and then I shall convert the transient response to the time domain. Here's the transfer function of the lowpass circuit: H(s) = \frac{\frac{1}{LC}}{s^2 +...

Given a metric tensor gmn, how to calculate the inverse of it, gmn. For example, the metric g_{\mu \nu }= \left[ \begin{array}{cccc} f & 0 & 0 & -w \\ 0 & -e^m & 0 &0 \\0 & 0 & -e^m &0\\0 & 0 & 0 & -l \end{array} \right] From basic understanding, I would think of divided it, that is...

Homework Statement Hi all, I'm struggling to find the Inverse Laplace transform of the following function: F(s) = (1+ 4e(-s) - 5e(-3s)) / s(s2 + 11s + 55), where F(s) is a Laplace transform Solution should be in terms of complex exponentials and unit step functions. Homework EquationsThe...

Hi all, I'm struggling to find the inverse Laplace transform of the following function: F(s) = (1+ 4exp(-s) - 5exp(-3s)) / s(s^2 + 11s + 55)Any help is appreciated. Thanks

Ok, I understand an inverse function sends a variable in the range to the corresponding value in the domain, but am not sure if what I'm thinking is correct... : For example: Let A be the set A = \{1,2,3,7,8\} ; B = \{4,5,6\} and the function f map A to B s.t f(1) = 4 f(2) =...

It doesn't seem like I have seen such a thing. I want to know if there's an inverse Curl operator? Let's say I was given the Curl of X = some function, now how can I solve for X ? How do I inverse the curl on both side of the equation? Thank you very much in advance.

Homework Statement cos(2tan-1(1/7)) equals- a)sin(4cot-13) b)sin(3cot-14) c)cos(3cot-14) d)sin(4cot-14) Homework Equations The Attempt at a Solution I am completely stuck in this one. I tried using the formula 2tan^{-1}x=tan^{-1}(\frac{2x}{1-x^2}). Using this formula i got...

Hi, I recently posted another question about a Laplace transform and now have a question about taking the inverse Laplace transform. Again, my professor did not cover this topic as well as I could have hoped for, and so I am stuck on this problem as well. Again, I understand the idea of Laplace...

Homework Statement i wanted to know ,why is the range of cot-1(x) (0,π), unlike tan-1(x) which has its range (-π/2,π/2). because for sin and cosec inverse range is same, for cos and sec inverse range is same. Homework Equations The Attempt at a Solution

2 very quick questions?? help needed asap 1. What is the inverse of the function ƒ(x) = ex? I think its 0? what do you guys think. 2. What is the lim (e^(x+h) - e^x)/h This one i tried and got a really weird answer can someone just give me just the answer??

Homework Statement 　　　2 -1 1 A = -1 2 -1 　　　-1 -1 2 Find A^-1 using Cayley Hamilton Theorem?Homework Equations The Attempt at a Solution http://i.imm.io/lyhB.jpeg I came thus far, 0 = -A^3 + 6A^2 - 11 + 6I How do I manipulate the above to get A^-1?

Homework Statement http://gyazo.com/966f3a03d71843a46a832e6508d6ca95 So when t> 0.5 or t<-0.5 the text says I1 and I2 cancel. Can I show this. When I tried, integration by parts gets me nowhere, so I looked up the integral of form e^x/x and apparently it has "no elementary derivative" -...

consider we have a map. what condition should have our map that it has inverse?

Homework Statement W(x,s)=(1/s)*(sinh(x*s^0.5))/(sinh(s^0.5)) Find the inverse laplace transform of W(x,s), i.e. find w(x,t). Answer: w(x,t)= x + Ʃ ((-1)^n)/n) * e^(-t*(n*pi)^2) * sin(n*pi*x) summing between from n=1 to ∞ Homework Equations An asymptotic series..?! The...

Homework Statement F(s) = s/((s-1)(s^2+1)) F(s) = (s/(s^2+4s+5))(e^(-3s)) Homework Equations Don't believe there are any. The Attempt at a Solution Not particularly sure. I can solve ((s-2)(e^-s))/(s^2-4s+3), but seem to be having problems with these.

I'm attempting to find the inverse laplace transform of \frac{25}{(1-s)^2*(4+s^2)} I get to this point but can't get the values of A B and C when equating coefficients. 25/(s-1)=A(4+s^2)+(Bs+C)(s-1) Also for a separate question: (s+1)/(5-4s+s^2) How do you find the inverse...

Homework Statement Dear All, I currently have a set of data which, when plotted on a scatter diagram, proves an inverse proportionality between two sets of data. (Please see attachment.) I now need to linearize the graph as to estimate the half-life of the foam. Homework Equations...

Homework Statement Having found the laplace transform of a differential equation. I must now find X(t). All of my work is attached. The problem I am having is fitting my function of s to my table of transforms. I tried using partial fractions but it took me in a loop.The Attempt at a Solution...

Hi, I know from basic math courses that inverse trig functions are multi valued (e.g. arctan(c)=θ+n*2∏). Now, if I solve a partial differential equation and I get an inverse trig function as part of my solution, does that mean solutions to the pde are non-unique? For example, if...

Homework Statement Inverse Fourier of: [ jω+2 ] / [ (jω)2 +5jω+9 ] where j = sqrt(-1) I tried using partial fractions but the denominator can't be factored...I tried completing the square on the denominator but I get a sum of squares. What can I try? I am sure I don't have to use the formal...

Trying to find the inverse of f(x)=2x^3+3x+2 I've written it as x=2y^3+3y+2 and am trying to solve for y, but I can't seem to factor anything out correctly. Anyone see how this can be solved?

I think I found a procedure (other than the extended Euclidean algorithm) to compute the multiplicative inverse of a number; possibly a simpler method. It goes like this: ***EDIT: Ah, dang. I made a mistake. It will only work for a prime modulus. Suppose we need to find x satisfying ax \equiv...

Hello Everyone :) I have been facing a little difficulty when encountering such kind of problems . i have also written down my line of thinking and approach which i take to solve them. So, please try to give me the correct line of thinking while solving such problems: 1. If A is invertible...

Homework Statement Suppose f: A → B is a function. Show that f is surjective if and only if there exists g: B→A such that fog=iB, where i is the identity function.The Attempt at a Solution Well, I believe for a rigorous proof we need to use the axiom of choice, but because I have never worked...

I was reading <crackpot link removed> and was wondering if the inverse cube law for magnetic force still applied for situations where the object being attracted isn't another magnet itself? E.g. if there is an electromagnet attracting an iron nut is the rule still inverse cube and not inverse...

Homework Statement y=x+(1/x) at y=17/4 Homework Equations The Attempt at a Solution y^-1: x=y+(1/y) differentiate: 1=y'+ln(y)y' 1=y'(1+ln(y)) y'=1/(1+ln(y)) put that over 1: 1+ln(y) plug in y: 1+ln(17/4) =approximately 2.447

Consider a function f(x) and its inverse g(x). Then (f \circ g)(x) = x and (g \circ f)(x) = x Are both these statements separate requirements in order for the inverse to be defined? Is it possible that one of the above statements is true but not the other? If so, could I see an...

Homework Statement This is from a physics problem, but my question is more mathematically oriented. After working through the problem, I arrive at the last step. Sin(x)=.967 The question says that there are two possible angles for x. The Attempt at a Solution arcsin(.967)...

My analysis text defines inverse functions only for bijections. But y = e^{x} is not bijective, so according to my book it's inverse ( ln x ) wouldn't be defined? Am I missing something or is my textbook just plain wrong? I use the text by Bartle and Sherbert. Thanks! BiP

Homework Statement The Attempt at a Solution Suppose we take an arbitrary polynomial in P_2 (R), call this a_0 + a_1 x + a_2 x^2 T(a_0 + a_1 x + a_2 x^2) = (a_0, a_0 + a_1 + a_2, a_0 - a_1 + a_2) Now, I was under the impression that I could construct a matrix for T by showing what...

Homework Statement Find the inverse laplace transform of \frac{3s + 7}{s^{2} - 2s + 10}Homework Equations completing the square. e^{at}sin(bt) = \frac{b}{(s-a)^{2} + b^{2}} e^{at}cos(bt) = \frac{s-a}{(s-a)^{2} + b^{2}} The Attempt at a Solution F(s)= \frac{3s + 7}{s^{2} - 2s + 10} F(s) =...

Homework Statement Find the derivative of[SIZE="4"] sec^{-1}(\frac{\sqrt{1+x^{2}}}{x}) Homework Equations [SIZE="4"]sec^{-1}=\frac{U'}{U\sqrt{U^{2}-1}} The Attempt at a Solution [SIZE="4"] U'=-\frac{1}{x^{2}\sqrt{1+x^{2}}} [SIZE="4"][SIZE="4"]U\sqrt{U^{2}-1}=...

Homework Statement Find derivative of [SIZE="5"]tan^{-1}(\frac{3sinx}{4+5cosx}) Homework Equations deriviative of[SIZE="5"] tan^{-1}=\frac{U'}{1+U^{2}} The Attempt at a Solution I found U'= [SIZE="5"]\frac{12cosx+15}{(4+5cosx)^{2}} [SIZE="5"]1+U^{2}=1+\frac{9sin^{2}x}{(4+5cosx)^{2}} I...

Homework Statement Find the derivative of: sqrt(x^2-4)-2tan^-1{.5*sqrt(x^2-4)} Homework Equations U'/1+U^2 U'=x/2sqrt(x^2-4) 1+U^2=x^2 The Attempt at a Solution I combined the above components but my answer is incorrect. I feel that I might have the wrong answer for...

Homework Statement Hi there I'm trying to solve this question: Homework Equations The Attempt at a Solution I figured i should just multiply them together and show that you get the identity matrix, but I'm having trouble cancelling out some of the terms. I'm not sure if I...

Using the laplace transform, find the solution to the differential equation: y'' + y' + y = 0 , y(0)=0, y'(0)=1 Using the laplace transform and its properties I end up with: f(s) = 1/(s2+s+1) How can I find the inverse of this/ does anyone know the inverse of it? Setting y=eax I got a...

Homework Statement Hi. I found in the answears that the inverse of function f(x)=3-\sqrt{x-2} is f^{-1}(x)=(3-x)^{2}+2 only if we restrict it to {x:x\leq3}. I understand that the restriction is needed because the found inverse is a parabola (and thus not one-to-one function). My general...

Derivative of inverse function at x=0 [SOLVED] Homework Statement Let f(x) = x + Ln(x+1), x > -1 Find \frac{d}{dx} f^{-1} |_{x=0}; Note that f(0) = 0 Homework Equations (f^{-1})'(x) = \frac{1}{f^{'}(f^{-1}(x))} (or) \frac{dx}{dy} = 1/\frac{dy}{dx} The Attempt at a Solution...

Find the inverse Laplace transform of $\displaystyle \frac{2s+7-e^{-2s}}{(s+1)^2}$.

Suppose that $\displaystyle f(x)=\frac{ax+b}{cx+d}$. What conditions on $\displaystyle a,\ b,\ c,\ d$ are necessary and sufficient in order that $\displaystyle f(x)$ coincide with its inverse function. My attempt: $\displaystyle...

Homework Statement The Attempt at a Solution So I observed: T(B) = λB T-1(B) = λ'B Also, T-1(T(B)) = λ'λB = B This implies, λ'λ = 1 And so, there should be a relation λ = \frac{1}{λ'}. Is that right?

Homework Statement How do I find the inverse of these functions step by step? y= e^-x^3 y= sin(1/x) I know the solutions but I don't know how to work with these two functions. Does anyone know the steps to finding the inverse of these?

Hi all I have been working on some unique solutions to advection-diffusion type problems. One inverse Laplace transform that I seem to continue to encounter is the following: Inverse Laplace[F(s)] where F(s)=[(1/(((s-α)^2)+β)*exp(-x*sqrt(s/D))] In their classic 1959 text, Carslaw...

Why are derivatives of inverse functions important? My students are giving me questions like: When would using the theorem be useful? Can't you just find the inverse function and take its derivative? I'm sure many of you know the type of question: "Who cares?" My answers are that the theorem...

Homework Statement What is the inverse of matrix A? A= (1) (2) (1) (2) (-1) (2) (1) (2) (1) Homework Equations The Attempt at a Solution The determinant works out to be 0 The inverse is 1/determinant x adj(A) Therefore the inverse is 1/0 x adj(A) So is the...

Let T: V-->W be a surjective linear transformation and let X be a subspace of W. Assume tat Ker(T) and X are finite dimensonal. Prove that T^-1 (X) = {v | T(v) is in X} is a subspace of V. Ok I absolutely suck at showing things are a subspace of something...I don't even know where to...

Hello everyone, I've been trying to figure out how to obtain the multiplicative inverse of an integer in Zn in Mathematica but I haven't found a way. Is there a way to do this anyone can help me with?

Homework Statement This is an integration of an inverse trig function. I don't see how they go from 1/2 to 1/4. I understand how they get the 1/2, du = 2dx, divide both sides by 2, but where does the 1/4 come from?

How does one use IFT to find the inverse of a function? I thought it was something like \int \frac{dx}{df(x)}dx. But that doesn't work with f(x)=x^2:\int \frac{dx}{2x}=\frac{1}{2} \log{x} \neq f^{-1}(x).

Assume that there is a original wall which does not have any defect inside. After an excitation of heat at one side of the wall, Ti is 37°C and To is 30° C. Thermal capacitance is assume 1. So the heat transfer is 7. For another condition, i want to find out if the wall has air pocket inside...