Exponential Definition and 1000 Threads

Homework Statement I have the following data which I would like to model using an exponential function of the form y = A + Becx. Using wolfram mathematica, solving for these coefficients was computed easily using the findfit function. I was tasked however to implement this using java and have...

I have the expression ##e^{\frac{1}{2} \log|2x-1|}##. I am tempted to just say that this is equal to ##\sqrt{2x-1}## and be done with it. However, I am not sure how to justify this, since it seems that then the domains of the two functions would be different, since the latter would be all real...

Homework Statement The question is given just like this: ##\frac{d}{dx}(exp\int_1^x P(s)\ ds)## = ? I assume they want me to find the derivative of the whole thing. Homework EquationsThe Attempt at a Solution I'm thinking the first step is: ##\frac{d}{dx}(exp\int_1^x P(s)\ ds) = (exp\int_1^x...

Let K be any Matrix, not necessarily the hamitonian. Is $$e^{-Kt}\left|\psi\right>$$ equal to $$e^{-K\left|\psi\right>t}$$ even if it is not the the eigenvector of K? I think so as i just taylor expand the $$e^{-Kt}$$ out but I want to confirm. In that case can i say that...

Calculation of $\displaystyle \int e^x \cdot \frac{x^3-x+2}{(x^2+1)^2}dx$

Homework Statement a= eD/R*T*G make a linear equations and calculate the value for D and G R=8,3 and constant D,G=constant T= variable Homework Equations y=ax+b y=numberax*bThe Attempt at a Solution ax= E/(R*T) x= 1/T a= E/R y= (E/R)*x+G I don't know how to move on and if this is even correct/

Homework Statement I think I am being stupid, I am trying to show that ## \int^{T}_{0} e^i\frac{2\pi(n-m)t}{T} dt = 0 ## [1] if ## n \neq m## ## = T ## if ##n=m##, ##T## the period. Homework Equations [/B] I am using the following ##cos## and ##sin## orthogonal...

Homework Statement [/B] Solve the equation ## e^{2x}+2=e^{3x-4}##Homework EquationsThe Attempt at a Solution I know by using Newton-Raphson method the problem can be solved, i however tried solving it as follows ##e^{3x-4}-e^{2x}-2=0, e^{3x}-e^{2x}.e^{4}-2e^{4}=0, p^3-p^2.e^4-2e^4=0...

I have a simple complex exponential signal of the form x(t)=ejωt. To find period of the signal I tested if x(t)=x(t+nT) for all n: ejωt=ejω(t+nT) ⇒ ejωnT=1=ej2πk where n and k are integers. Then I find a general period expression as T=2πk/ωn Period T means it is the least time a signal...

1. Homework Statement Find derivative of y=e^(cos(t)+lnt) Homework EquationsThe Attempt at a Solution So just using the chain rule: y'=e^(cos(t)+lnt)*(-sin(t)+1/t) The answer in the back of the book is y'=e^(cos(t))*(1-tsin(t))

I want to create a binary matrix (${X}_{m*n}$) containing $C$ ones ($||X|| = C$). Additionally I want to have the number of elements of each row ($m$) to have an exponential form. This is: for each row the number elements needs to be equal to $e^{alpha * i}$ or in symbols: ||${X}_{i}$|| =...

Homework Statement If ##r_1, r_2, r_3## are distinct real numbers, show that ##e^{r_1t}, e^{r_2t}, e^{r_3t}## are linearly independent. Homework EquationsThe Attempt at a Solution By book starts off by assuming that the functions are linearly dependent, towards contradiction. So ##c_1e^{r_1t}...

Homework Statement I want to show that ## \sum\limits_{n=1}^{\infty} log (1-q^n) = -\sum\limits_{n=1}^{\infty}\sum\limits_{m=1}^{\infty} \frac{q^{n.m}}{m} ##, where ##q^{n}=e^{2\pi i n t} ## , ##t## [1] a complex number in the upper plane.Homework Equations Only that ## e^{x} =...

The wave function is an exponential function, if I plot the real part of it, I don't get a wave graph like sine or cosine function, Why the wave function is not represented by a trigonometric ratio instead. Also, the wave function cannot be plotted since it is imaginary, why is it imaginary? Thanks

hi everyone initially I really want to put into words that there is absolutely no source related to following probability in poisson process and distribution $$P(S^1_A<S^1_B<S^1_C)$$ or $$P(S^n_A<S^m_B<S^k_C)$$ where $$S^1_A = \text{first arrival of A event}, S^1_B= \text{first arrival of B...

Hi, I've been reading Roger Penrose's Road to Reality during my free time, and I am trying to do all the proofs I possibly can, although I am quickly reaching my limit. Would somebody help me prove this? h(x)=0 if x ≤ 0 h(x) = e-1/x if x > 0 Thank you in advance :)

Consider the operator Ô, choose a convenient base and obtain the representation of \ exp{(iÔ)} Ô = \bigl(\begin{smallmatrix} 1 & \sqrt{3} \\ \sqrt{3} & -1 \end{smallmatrix}\bigr) Attempt at solution: So, i read on Cohen-Tannjoudji's Q.M. book that if the matrix is diagonal you can just...

So I'm trying out various practice problems and for some reason I can't get the same answer when it comes to problems involving natural exponentials. Here's the problem A type of lightbulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of...

this is not a homework question, I just want to make sense of the equation here. Assuming matrix A is diagonal, If A_hat=T'AT where T' is an inverse matrix of T. e^(A_hat*t)=T'e^(At)T which implies, e^(T'AT*t)=T'e^(At)T we know that e^(At) is a linear mapping, therefore if we convert f to...

Mod note: Changed title from "Differential Euler's Number" 1. Homework Statement Find the derivative. f(t)=etsin2t The Attempt at a Solution f'(t)=etsin2t(sin2t)(cos2t)(2) However the book seems to say that there should be an extra "t" in the solution. Some help?

Homework Statement Using experimental data, I am trying to solve the following equation for ##T_2## $$M(t)=M_0 e^{-t/T_2}. \tag{1}$$ Here ##M_0## denotes the initial value. There were 8 data points collected for ##t## and ##M(t).## Here is the resulting graph: The data and equation (1)...

Homework Statement Write the given numbers in the polar form ##re^{i\theta}##. ## \frac {2i} {(3e^{4+i})} ## Homework Equations ## z = re^(i\theta) ## ## \theta = Arg(z) ## ## r = |z| = \sqrt { x^2 + y^2 } ## The Attempt at a Solution I'm not really sure how to go about the exponential...

Homework Statement 2x=1/ square root of x. Homework Equations [/B] None that I feel ought to be included. The Attempt at a Solution To answer the question I graphed 2^x and 1/sqrt x individually. They intersect at an x value of 0.5, so x= 0.5. The problem is that while the answer was...

Homework Statement How is ## e^log√(1-x^2)## equal to ##√(1-x^2)?##Homework EquationsThe Attempt at a Solution taking ln on the function, ln√(1-x^2). lne⇒ ln√(1-x^2) ....

Homework Statement In 2003 the city of spring field had a population of 250000 the population is expected to double by 2025, how many people in 2015? Homework EquationsThe Attempt at a Solution A=Pb^t The initial is 250000 and b is 2 because it doubles however I am unsure of what the exponent...

The problem Solve ## e^x-e^{-x} = 6 ## . The attempt $$ e^x-e^{-x} = 6 \\ e^x(1-e^{-1}) = 6 \\ e^x = \frac{6}{(1-e^{-1})} \\ x = \ln \left( \frac{6}{1-e^{-1}} \right) \\ $$ The answer in the book is ## \ln(3 + \sqrt{10})## Could someone help me?

Hi there! First Post :D In a recent CM module we've been looking at coupled oscillators and the role of time translational invariance in the description of such physical systems. I will present the statement that I am having trouble understanding and then continue to elaborate. In stating that...

Homework Statement Homework Equations A = P(1+i)^n The Attempt at a Solution Here is my attempted solution, can someone please verify if my method is correct! Thanks in advance![/B]

Homework Statement Homework Equations The Attempt at a Solution here is my attempted answer, can someone please verify if my method is accurate and if my solution is correct? thanks for the help!

Hi there. I was trying to implement Numerov method for solving second order differential equations (you can see some information of Numerov algorithm at here: https://en.wikipedia.org/wiki/Numerov%27s_method ). At the beginning I've used a uniform grid mesh, all points equally spaced. I'm...

Hello, I am looking for approximated or exact solution of \begin{align} I = \int_R \exp(cx^3-ax^2+bx)dx \end{align} where $a,b,c$ are complex numbers defined as: \begin{align} c &= \frac{1}{3}i\pi\phi'''(t) \notag\\ a &= \dfrac{1}{2\sigma^2}-i\pi \phi''(t) = re^{i\varphi}~~\text{with}~~~ r =...

I need to convince myself that ##e^{ikr\text{cos}\ \theta}=\frac{\text{sin}\ \theta}{kr}##. Could you please help me with it?

If I rearrange an equation invoving exponentials of operators and I take ex to the opposite side of the equation it becomes e-x. What happens if I try to take eA to the opposite side ? I know a exponential of operators can be expanded as a Taylor series which involves products of matrices but...

The expansion of the inflationary universe is said to be roughly exponential. Why is it called "roughly" exponential?

Homework Statement If ##a, b \in \{1,2,3,4,5,6\}##, then number of ordered pairs of ##(a,b)## such that ##\lim_{x\to0}{\left(\dfrac{a^x + b^x}{2}\right)}^{\frac{2}{x}} = 6## is Homework EquationsThe Attempt at a Solution So, this is a typical exponential limit...

Hello, I have the following code in Mathematica, and it gives the following error: NIntegrate::ncvb: NIntegrate failed to converge to prescribed accuracy after 12 recursive bisections in x near {x} = {0.000156769}. NIntegrate obtained 0.21447008480474927` and 5.637666621985554`*^-13 for the...

Homework Statement Hi, I have come across this equation in modelling exponential growth and decay. I am wondering if it is possible to solve it algebraically or not? Homework Equations 8000-1.2031 * e^ (0.763x)=(0.5992×e^0.7895x) The Attempt at a Solution Brought all e^(ax) values to one...

After following the logical steps to derive something, I reached to the following integral: \int_0^{\infty}\frac{1}{x^2}\exp\left(\frac{A}{x}-x\right)E_1\left(B+\frac{A}{x}\right)\,dx where ##E_1(.)## is the exponential integral function, and ##A## and ##B## are non-zero positive constants. I...

Hello, I am enrolled in calculus 2. Just having started a section in our textbook about integration by partial fractions, I eagerly began trying to use this integration technique wherever I could. After messing around for multiple days, I ran into this problem: ∫ 1/(x^2+1)dx I immediately...

In my electrical engineering textbook, they have an entire chapter devoted to the complex Exponential. I don't really understand it, nor do I understand its importance. I know it is extremely important, and need to understand why, and what exactly it is, and the wording of the online resources...

Homework Statement Calculate activation energy and pre exponential factor, i need help with the pre exponential factor Homework Equations Temperature °C -20 = 253 k -10= 263 0=273 10=283 20=293 Rate const. s-1 1.15 3.85 11.3 28.7 74.0 The Attempt at a Solution i already plotted the graph on...

I recently completed a lab using an online projectile simulator about the range of projectiles. I launched a projectile with different initial speeds (5 m/s, 10 m/s, 15 m/s, 20 m/s, and 25 m/s). For each trial, I did the launch with and without air resistance and I plotted Range (with Air...

Homework Statement Solve ##y=\mathrm{exp}(\frac{-x\pi}{\sqrt{1-x^2}})## for x when y = 0.1 Homework Equations ##\mathrm{ln}(e^x)=x## The Attempt at a Solution ##\mathrm{ln}(0.1)=\frac{-x\pi}{\sqrt{1-x^2}}## ##(\frac{-\mathrm{ln}(0.1)}{\pi})^2=\frac{x^2}{1-x^2}##

2 = X to the power x to the power x, until infinity. I really need to know how its possible for the answer to be √2

Plz give me an easy explanation I do know about the differentiation and second differentiation. I just don't get how that negetive sign comes in front of the exponent in the second differentiation

Hello, folks. I'm trying to figure out how to take the partial derivative of something with a complex exponential, like \frac{\partial}{\partial x} e^{i(\alpha x + \beta t)} But I'm not really sure how to do so. I get that since I'm taking the partial w.r.t. x, I can treat t as a constant term...

How do we get (6.265)? Shouldn't we have ##exp(-i\frac{\alpha}{2}\hat{n}.\sigma)=\cos(\frac{\alpha}{2}\hat{n}.\sigma)-i\sin(\frac{\alpha}{2}\hat{n}.\sigma)##?

Homework Statement https://dl.dropboxusercontent.com/u/17974596/Sk%C3%A6rmbillede%202016-02-02%20kl.%2007.35.26.png I want to find variance matrix and expected variance vector of Y=(Y1,Y2). Y1 and Y2 are independant. Γ is the gamma function and ϒ is a known parameter. λ1>0 λ2>0 and ϒ>0...

Let's say my probability function is given by: p(y1,y2)=Γ(y1+y2+γ)/((y1+y2)!*Γ(γ)), when γ>0 is known. I suppose it is from an exponential family but I can't write in canonical form because I'm only familiar with exponential family with one variable so I'm confused now when there's to variable...

Homework Statement Find the first and second derivative of the following function: F(x)=e4ex Homework Equations d/dx ex = ex d/dx ax = axln(a) The Attempt at a Solution I know the derivative of ex is just ex, but I'm not sure how to go about starting this one. I'm near certain I need to use...