Inverse Definition and 1000 Threads

Homework Statement 1/(u^2+4) Homework Equations The Attempt at a Solution I know that 1/(x^2+1) is the derivative of the inverse tangent function, and that is proved by using tany = x, derivative of both sides with secx=(1+tan^2x) and tan^2x = x^2. I don't know how to use the...

What use is the inverse matrix? I would not use it to solve linear systems but there must be some concrete or real life applications where it is used.

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I have researched this area a little bit and now I am a little worried because three different websites have gave me three different answers. Some functions matched, but others didn't. My general consensus is inverse Sin= 1 and 4 quad inverse Cos= 1 and 2 quad inverse tan= 1 and 4 quad...

This is in reference to the Chapter 10. of P. R. Halmos's Naive Set Thoery, namely 'Inverses and Composites'. He speaks of two equations in that section. 1. Let f be a function from X to Y. The inverse of a set is defined as another set as follows. f^{-1}(B) = {x\inX:f(x)\inB}. The first...

Homework Statement Let a and b be elements of a group,with a^2=e , b^6=e and a.b=b^4.a find its order and express its inverse in form of a^m.b^n Homework Equations The Attempt at a Solution (ab)^2=(ab)(ab)=(ab)(b^4.a)=a(b^5)a (ab)^3=a(b^5)a(ab)=a(b^5)(a^2)b=a(b^6)=ae=a it...

Homework Statement (A somewhat similar question to my last one). Let J be the ideal of the polynomial ring \mathbb{Q}[x] generated by x^2 + x + 3. Find the multiplicative inverse of (3x^3 + 3x^2 + 2x -1) + J in \mathbb{Q}[x]/JHomework Equations The Attempt at a Solution I think I need to apply...

Homework Statement Find the inverse function of f(x)= 2x + lnx 2. The attempt at a solution So usually i would start out with y= 2x+lnx (finding x terms of y) and then switch x and y... but i can't figure out how to find x. doesn't seem to be possible to factorize this... are there other...

How do I take the inverse laplace transform of something that looks like this? It's part of a larger piecewise-defined second order differential equation, but this is the part I'm stuck on. (-4s-1)/(4s^2 + s + 4) Completing the square doesn't work for the bottom, so I figure I need to...

I don't understand why all authors of this proof assume that Df_a = id_n, how doesn't this destroy generality? For example, see https://www.physicsforums.com/showthread.php?t=476508. The λ in his post (and the post he quotes) is always Df_a (its not stated in that post, but in the book and the...

> f(x) \ = \ \dfrac{1 - \sqrt{x}}{1 + \sqrt{x}}

Hello Everyone! I've been trying to solve an equation and got to this place: $\sum _{j=1} ^K (x_j - b_j) = 0$ which gives $e^T x = e^T b$. Now I need to solve for $x$ i.e. find $x$ in terms of the b. How can I do that? Thank you for the help!

Homework Statement Find the inverse of exp(y-x)+5 2. The attempt at a solution I think the solution is y-ln(x-5) but I can't think of how to solve it to get that. I don't know what to do about the x and the y being together.

Hello all, I already know that the radiant intensity of a point light source falls off with the inverse square of the distance to the source. This, however, only happens in a vacuum. My question is, what is the more general law for a point source inside an opaque medium with a known...

Hi everyone, I'm trying to solve an exercise in which I need to find x(t) considering that X(ω) = cos(4ω). So, I need to find the Inverse Fourier Transform of cos(4ω), but I don't have the inverse Fourier transform table. So, I thought about applying the duality property. If x(t) <-->...

I've never been able to visualize how the tangent to a curve and the area under a curve are inverses of each other, can anyone give some intuitiveness to this?

Homework Statement See attached file. Homework Equations The Attempt at a Solution I've only been able to do part (a) of this question. I ended up with: tanz= i ({\frac{1-e^{(2iz)}}{1+e^{(2iz)}}}) I'm not sure how to approach the next two parts. If anyone could give me any...

Homework Statement Evaluate the following: Sin^-1(sin(19*pi/7) in terms of pi The Attempt at a Solution i can't see any other way apart from the functions cancel to give 19pi/7 but checking on wolfram gives 2*pi/7, can anybody explain or help? Thanks

Homework Statement I have to find the inverse of the 1-D momentum operator. Homework Equations The Attempt at a Solution Here's my solution: Pψ(x) = -iħ dψ/dx P-1[Pψ(x)] = P-1[-iħ dψ/dx] [P-1P]ψ(x) = -iħ [P-1 dψ/dx] Iψ(x) = -iħ [P-1 dψ/dx] ψ(x) = -iħ [P-1 dψ/dx] By...

I have a graph f(x) = 3(x + 1)^2 - 12 , I have sketched this graph (Not shown) hand it is a parabola with a y- intercept at - 9. the vertex being - 12. The image set is a closed interval {- 12, infinity} Sorry no square brackets and no sign for infinity. I am asked to explain why the function...

Homework Statement I am more trying to figure out how to solve generally rather than solve this specific problem. Nevertheless this problem could be given as: Solve the matrix for A and B. Homework Equations \begin{pmatrix} 1 & 1 \\ 0 & 0 \\ 0 & 2 \\ 2 & 0 \\ 0 & 0 \\...

Homework Statement I can't figure out what the limits of integration should be; if a transfer function is given as follows: h(ω)=1 if 1<|ω|<2, 0 otherwise 1) find the impulse response 2) if the input is white noise of intensity σ² find the variance of the output signal 3)state...

How can I determine what the smallest value of a χ2 statistic must be to reject the null hypothesis at α = 5%, for a distribution with 9 degrees of freedom? Thanks in advance.

Can someone please do a step by step proof for this or send me a link to a step by step webpage. Thank you very much Cosh^(-1 ) A/x=( x √(X^( 2 )+A ))/2a my attempt=> Cosh^(-1 ) = y A/x = Cosh^(-1 ) A/x = Sechy A/x= (2/(e^2 + e^-2))

Homework Statement laplace inverse of (40/(s^2+4s+5)^2)? Homework Equations I completed the square in the denominator to get 40/((s+2)^2+1)^2 I know that I will get cosines and sines from the shape of it in the laplace inverse; however I'm stuck. The Attempt at a Solution

Dear folks! Please help me this problem. I want to calculate inverse of lower triangular matrix in a fastest way. I use Mathematica and function LinearSolve. It did well. But because the matrix is lower triangular matrix. It is very special. So, I want to make a function called...

What will be a well recognized introductory book on statistical inverse problems, for undergraduate mathematicians and statisticians? The book should be written in elementary linear algebra and probability theories, i.e., no functional analysis, no measure theory, etc. Thank you.

Hi all, When there are two variables x, and p related via any differentiable function, we have the following identity: \frac{dx}{dp}\frac{dp}{dx}=1 When it comes to partial derivatives we can NOT say \frac{\partial x}{ \partial t}\frac{\partial t}{\partial x}=1 . However I have seen the...

In a few books on Operations Research, I have found a reference to a method of finding the inverse of matrix using a method called as 'Product Form'. From the context, it looks like the product form method is used for finding the inverse of the basis matrix in a simplex table. The method may or...

Homework Statement Let f(x) = sinh(x) and let g be the inverse function of f. Using inverse function theorem, obtain g'(y) explicitly, a formula in y. Okay the Inverse function Theorem says (f^-1)'(y) = 1/(f'(x)) If f is continuous on [a, b} and differentiable with f'(x)\neq0 for all x\in[a...

$\displaystyle \int \frac{x^2\cos^{-1}\left(x\sqrt{x}\right)}{(1-x^3)^2}dx$

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.

Homework Statement Hello, i am trying to achieve inverse kinematics of a spherical manipulator (three revolutes in orthogonal axes) and the first angle (from geometry) is determined by something like this θ1=atan2(x,y) (i use maple so the function is something like θ1=arctan(y,x)); when i...

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...