Inverse Definition and 1000 Threads

Hi all, I've been trying to solve the following I = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \frac{x}{(x^2+y^2+d^2)^{\frac{5}{2}}} e^{-i(kx+\ell y)} \ dx \ dy where d,k,\ell are constants. I haven't been able to put this into a tractable analytic form and I figured I'd consult all...

Hello how can we know with the definition of inverse function this function is inverse function or not? ? another questions. this function is inverse function because but if we have this function we can't do the same approach.why?(and it isn't a inverse function)...

I was asked this question on a test I just took and I was kinda stumped. I worked it out but I think I did it incorrectly so I was hoping for some input. Thanks. 'A' is a 3x3 matrix and 'I' is the identity matrix for a 3x3. Find the Inverse of 'A' given...

Homework Statement I'm trying to solve the derivative of this equation: 1-(x*arcsin(x))/√(1-x^2 ) I've straight away disregarded the 1 as it will be 0 so I'm left with -(x*arcsin(x))/√(1-x^2 ). The Attempt at a Solution I've applied the quotient rule and labelled U= -x*arcsin(x) and...

I understood that for a direct proportion such as "if 6 mangoes cost $12, then how many dollars worth are 12 mangoes?", we have to first divide 12 by 6 to get the no. of divisions of 6 in 12 i.e. precisely 2 and then as 1 division is worth $12 we multiply the two divisions with $12 and that's...

Hi. I am reviewing for an exam, and this is a topic that I did not go through very thoroughly. I understand how to calculate the derivative of an inverse function when I am given a point, as I simply use the equation (1/f((f^-1))'. So if I am given the equation y=x^3, for example, and am asked...

Hello All: Suppose I have a completely known linear system: A*x=b. I know the matrix A, and an x and the associated RHS vector b (and it is non-trivial). Is there some tricky way to directly determine the inverse of A without performing an inversion by typical means (Gauss elimination, LU...

Homework Statement Let A be an m x n matrix, and suppose there exist n x m matrices C and D such that CA = In and AD = Im. Prove that C = D. Homework Equations The Attempt at a Solution I think it's obvious that C=D=A^(-1). But I'm having trouble proving it since I cannot prove...

Hi guys :) I'm looking to get a jump start on my uni course and have been going through some topics on my own before classes start in the Fall, I've reached the point of Laplace Transform and Fourier maths - and it's tough! I have a small question on an inverse laplace transform equation in...

Homework Statement find dz/dy(partial) z= tan-1(y/x) Homework Equations The Attempt at a Solution z= tan-1(y/x)let u=y/x z= tan-1(u) dz/du = 1/ (1+u2) so dz/dy = dz/du (du/dy) du/dy = 1/x so dz/dy = (1/1+u2)(1/x) = 1/ 1+ (y2/x2) * 1/x = 1/ x + (y2/x2)x) = x / x + y2but I should be...

Homework Statement f(x)=3+x2+tan((πx)/2) where -1<x<1...then find f^-1(3) Homework Equations y=3+x2+tan((πx)/2) The Attempt at a Solution i jave ried to solve first for x and then interchange the x and y,bu i am having problem with the trignometric identity used here...

Hi everybody I have a question that I have a guess for the answer but I want to be sure I have an identity C=A*B where A,B,C are matrices and in general they are not square is there a way to find A in terms of B and C by using pseudo inverse matrix or using pseudo inverse might help me in...

Homework Statement We did an experiment using resistance putty and a multimeter. We changed the radius of the putty but kept the length the same. We recorded the resistances at different radius'. I know that physics theory says that resistance is inversely proportional to cross-sectional...

Hello again. First off, I wasn't sure how to say this in the title but I'm not taking the inverse Laplace transform of a unit step function. I'm taking the Laplace transform of something that comes out to the unit step function. I have this question, which is a similar version of the...

Hello, this is related to my research on RCW(FMM) analysis of light shone onto crossed gratings. main question: can you exploit having matrix A and its inverse A^{-1} to calculate the eigen vectors/values of A in a more effective way? backgroud: so my problem is this: I have an unusual...

I am aware that, in statistics, things get difficult as soon as they get nonlinear. And taking the reciprocal of a quantity is a nonlinear operation. I have some data that would form a nice looking straight line, except for random error scattering it around the line. I have a total of about...

y = 3^-x + 9^-x ln(y) = ln(3^-x + 9^-x) don't know where to go from here.

Hi, so this isn't a question, it's just an example that they've given, but I don't understand the explanation given. You have : y = x^2 - 4 x = y^2 - 4 y^2 = x + 4 y = ± sqrt(x+4) I don't get why there is a ± symbol there. My book says that it's necessary because there are two...

Hi, I am trying to solve the integral of the Inverse Gamma Distribution. Does this equate to 1 as it is a pdf? Thanks

i read this sentence like a 100 times and i still don't get it please can anyone help me?? PEAK INVERSE VOLTAGE (PIV): PIV is the maximum reverse bias voltage which can be applied safely to a diode without its breaking down. Beyond this voltage a diode breaks down they say the PIV must be...

Homework Statement Problem reads: find inverse Laplace transform of f(t) of F(s)=(2s+3)/(s(s2+7s+10) What is the value of the function f(t) at t=0 and t=∞?Homework Equations Inverse laplace transformThe Attempt at a Solution I solved F(t) down to F(t)= .3/s+0.166/s+2-0.465/s+5 thus lead me to...

I have written some routines that compute the 2D inverse Fourier transform, if anyone thinks that this may be useful at all then please let me know and I will gladly post the code.

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...

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

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 \\...

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: [SIZE="3"]\frac{dx}{dp}\frac{dp}{dx}=1 When it comes to partial derivatives we can NOT say[SIZE="3"] \frac{\partial x}{ \partial t}\frac{\partial t}{\partial x}=1 . However...

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...

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