Exponential Definition and 1000 Threads

please help me! the variance of the score function in exponential distribution Homework Statement My question is about exponential function, with its density function known as f(x;theta) = (1/theta) e^(-x/theta) for all x>0. where E(x) = theta, var(x) = theta^2 My question is, what...

The signal x(t) = e^{jt} is periodic. The signal x(t) = e^{-t}e^{jt} is not periodic. The decaying exponential makes the complex exponential decay and converge toward zero, but why is it not periodic? Also, this signal is not considered time limited since it never actually reaches zero...

Homework Statement \int^{\infty}_{0} e^{-y} dy = 1 Homework Equations The Attempt at a Solution Why is this equality true? I understand that the integral and derivative of e^y is always e^y, but I can't make out why this definite integral is equal to 1. I graphed it using a...

Homework Statement 2n=n2 Homework Equations The Attempt at a Solution I know the solution is 2 and 4. But I have no idea how to solve it without guessing...

Homework Statement Write the function for each graph described. Exponential function with y-intercept of 3 and horizontal asymptote of y=0Homework Equations None The Attempt at a Solution I used the base equation f(x)=a^(x+h) + k to get f(x) = 3^(x+1) Was this right? Also, I used guess and...

Homework Statement Hey guys. How do I solve this integral? http://img816.imageshack.us/img816/208/68315659.png I've not been doing this for a long time :) Thanks a lot. Homework Equations The Attempt at a Solution

find x for y=5 y = -(((e^x)/(e^-x))/2) + ((e^x)/(e^(-3x)) all i did was a^m / a^n = a^m-n i get here y = -1/2(e^(2x)) + (e^(4x)) after this i get iffy and want to make sure i can do what i did. 5 = -1/2(e^(2x)) + (e^(4x)) ln|5|= -1/2(ln(e^2x)) + ln(e^4x) ln|5|= -1/2(2x) + 4x...

I've been struggling with this problem for more than 4 days now: Let A, B and C be exponential distributed random variables with parameters lambda_A, lambda_B and lambda_C, respectively. Calculate E [ B | A < B < C ] in terms of the lambda's. I always seem get an integral which is...

Homework Statement If X is a random variable with density function: f(x) = \lambdae^{-x \lambda}where X>=0.Homework Equations Why is the expected value of X, or E[X] = \frac{1}{\lambda}?The Attempt at a Solution E[X] = \int x*(\lambdae^{- \lambda}^{x}) dx, where the integral is from 0 to...

Homework Statement I'm working out different pathlengths for different solids but I'm stuck on the following integral: Homework Equations \int x*exp(-C*sqrt[1-x2/A2]) dx exp = exponential func sqrt = square root C and A are constants The Attempt at a Solution I tried to work...

I have some questions I have labeled below: I believe that the coefficient of static friction, (let's call it Csf), equals the maximum force of static friction (before it slips), Fsmax, divided by the force bringing the two surfaces together (a force in the direction of the normal to their...

I'd like to do one of two things: 1: Find an example of a non-diagonal matrix whose matrix exponential (defined in terms of series) is diagonal. 2: Prove that no such examples exist. I'm working with matrices over the complex field. My gut tells me that 2 is the way to go. I'd really...

I've tried and searched for a long time, and I haven't been able to prove or find a proof that the following sequence converges (without using another definition of the exponential function): \forall x \in \mathbb{R}. Prove that: \lim_{n \rightarrow \infty} (1+ x/n)^n exists. I can...

Hi i was wondering if anyone could help me with a fairly simple integration. \int exp(iab/c)exp(-iaz) da Where the integral is from 0 to infinity Im not sure how to proceed with this and am basically teaching myself Thanks in advance for any help.

Homework Statement Greetings - can someone please check my work, many thanksHomework Equations If x = 12.4 Find the value of ... correct to two sig fgures 8^(4x/3) / log(base 10) (5x-3/x^0) The Attempt at a Solution = 8^(16 8/15) / log(base 10) (5(12.4)-3 / 1) = 4.8 x 10^14 (via calc...

I just want to make sure that I have this in the correct order. The book I have is very unclear. e^x + e^-x = 6 e^x + 1/e^x = 6 e^2x + 1 = 6e^x e^2x/e^x + 1 = 6 x = ln 6 Thanks.

Hi, I need to solve the equation e^z = -3 The problems arises when i set z to a+bi e^a(cos(b) + isin(b),~b = 0 Then I am left with e^a = -3 However you're not allowed to take the log of a negative number. Also i know that cos(\pi) + isin(\pi) = -1 Obviously 3e^{(\pi*i)} is a solution, but...

Homework Statement Turn y = y(0) * e^(-kt) into a polynomial. Homework Equations The Attempt at a Solution I have no idea of how I would go about doing this. I know you can use taylor series to approximate it, but is there any other way? Thanks, Darthxepher

Dear all, I have exponential integral with polynomial. I tried to solve it but I could not. the integral is :Homework Statement The integral equation is: \int_{-\infty}^{\infty} (ax^2+bx+c) e^{ax^2+bx+c} dx$ Homework Equations The Attempt at a Solution Can anyone help me please. Thanks...

Is it possible to integrate this function \int {e^{x^2}} dx \int \left (y^2) e^{y^2} dy The book says there is no direct method to solve this type of integrals but there is no hint how to solve this.Any one please help. Thanks :) Sorry for the latex code i have put the integration...

Homework Statement Solve for x: 4x+7=18 Homework Equations It becomes 4x=11 The Attempt at a Solution I have no idea where to go from here. We never had a problem with such an immovable number such as 11 to work with. Calculators are not allowed to be used either.

Hello every one, I was doing my research and then I simply struck at a point. The point is that i do not know how to solve the following Integral. I am not at all bad at doing math but some times I got blanked. so, here is the Integral, Integral (infinity,u) exponent^(-u) du...

I have to calculate the exponetial of a large (on the order of 10^5) negative number. I tried using exp(), the exponential function from the cmath library, but I get an answer of 0. So, I tried to use the power series for the exponential function. For numbers from -1 to -14, I get answers which...

Hi I'm self-teaching calculus and I'm looking at exponential growth and decay. The differential equation for relationships like these if this was related to time is dP/dt = -kP i.e. the rate of change in P with time decreases at a rate which is proportional to the amount of P present. I can...

Homework Statement - The following table gives the population of a city over time: Homework Equations I know this equation: y = a(b)x and exponential growth: b = 1 + growth rate and b = 1 - decay rate The Attempt at a Solution I know from back in chapter 2 that first...

Homework Statement I have problem solving an integral equation of the form Homework Equations \int_{0}^{\infty}(a\Lambda^2/(\Gamma(\gamma-\Lambda)^2))exp(\Lambda\gamma/(\Gamma(\gamma-\Lambda))-(\gamma-b)/c)d\gamma The Attempt at a Solution I have tried to solve it by...

Sorry if this might be in the wrong section, but I wanted someone's opinion on the formation of rust. Do you think that the rate of formation of rust on iron/steel is an exponential growth?... --- Also, some extra. I'm doing an EEI on rusting - basically, I'm trying to find the best...

Hi there,Struggling with this problem, anyone know how this might be solved? (e^(r-0.04)^(5/12))(0.9463) = (e^(r-0.04)^(11/12))(0.95152) and solve for r Ans: r~2.90% Would really appreciate it!

Hello, How can I find the limit of x^{k}\mathrm{e}^{-ax^n} for x\to +\infty. a,k,n are positive reals. I even have troubles solving it for k=1, a=1, n=2. Any hint?

Hi everyone, here is this integral I can't find solution: \int_0^\infty \frac{x e^{-x}}{A+Bx} dx A and B are constants. I'm going crazy, I don't think there is even an analytical solution.

Homework Statement Hi, I need to find the spectrum of the following function: i=I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi 100000t))}{0.026}}-1]Homework Equations the Fourier Transform would be: \int_{-\infty }^{\infty }I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi...

Hi, I am trying to find an analytic solution to the following double integral...

Homework Statement I did the question with help, but did not understand why did we multiply e^-i(x/2) How do I know what to multiply for getting the real part of a complex number in exponential form? Homework Equations The Attempt at a Solution

Hi, Does anyone know of an analytic solution for the integral \int_{0}^{\pi}\sin\theta\exp\left(a\sin^{2}\theta+b\sin\theta\right)d\theta Thanks.

Hello, for continuous compouding (in the exponential growth and decay) the function for interest after t years is: A(t) = A0*e^rt A0 should be read A at time 0 in the book, they say when you differentiate this function this is what you get dA/dt = r*A0*e^rt = rA(t) I don't see...

Homework Statement Derive an equation of the form y=ax^b to model the given data: (35, 0.01) (28, 0.03) (20, 0.1) (15, 0.3) (11, 1) (9,3) (6, 10) (4.5, 30) Homework Equations Well, I know the answer is y = (7790 +/- 1246)x^(-3.698+/-0.1036) because that's what LoggerPro spits out, but...

I forgot how to derive the mean of exponential random variables follow the chi square distribution with degree freedom 2n. Don't know where I got it wrong. Anyone have a clue how to do it? Thanks

Homework Statement a.) A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean u = 1000, find the probablity that both of the lamp's bulbs fail within 1000 hours...

I have a density function: f(t) = L * e-L(t-t0) * u(t-t0) where u(t) is the unit step function. And I have a column vector X, which is randomly chosen samples from f(t): X = [x1 x2 ... xn]T How can I estimate the unknown values t0 and L from this X vector?

This is part of double integral. I just can't seem to figure out what I'm doing wrong. The inner integral comes out to be: \int_0^\infty{e^{-xy}dy} I emailed my teacher to help me through it, and he says this should integrate down to 1/X but I can't seem to figure out how. I'm no good...

Homework Statement ex / (1 + ex)

Homework Statement Solve the following equations using simultaneous equations Homework Equations 32x\times23y=17 4x\times5y=37 Appologies for the bad equation set-up. The large 'x' is a multiplication sign. The Attempt at a Solution My attempt was to divide both of the...

Homework Statement A particular species of mollusk is distributed according to a Poisson process with an unknown density of lambda per cubic meter of water. A sensor is constructed that can detect these species that are within 4 m, and n readings are collected over a year to try and measure...

Homework Statement IF X has an exponential distribution with parameter \lambda, derive a general expression for the (100p)th percentile of the distribution. Then specialize to obtain the median. Homework Equations X.exp(\lambda)=\lambda e^{-\lambda x} for x>0 p=F(\eta (p)) =...

Homework Statement A tissue culture grows until it has an area of 9 cm^2. Let A(t) be the area of the tissue at time t. A model of the growth rate is that: A'(t) = k*(sqrt(A(t)) * (9-A(t)) a. Without solving the equation, show that the maximum rate of growth occurs at any time when...

e ^ (-2 ln |x + 1|) = e ^ ln [1 / (x + 1)^2] how can this happen? can anyone explain to me the process of this equation..

Write the following log equations as exponential equations and vice-versa. 1.) ln 0.5 = - 0.6931 Differentiate with respect to x. 2.) y = e^x(sin x + cos x)

Homework Statement To encourage buyers to place 100-unit orders, your firm's sales department applies a continuous discount that makes the unit price a function p(x) of the number of units x ordered. The discount decreases the price at a rate of $0.01 per unit ordered. The price per unit for a...

Find the real part of the complex number: (1-12i)e^{-2+4i} I know that z = a + ib can be rewritten as z = |z|e^{i\theta} but that doesn't help because the coefficient of the e is not a scalar value, rather a complex number. Thanks Tom

Say we have a decay of the form A e^{-a x} + B e^{-b x}. I haven't had much luck trying to calculate the half-life of such a decay (I'm not sure it's possible, analytically), i.e. solve A e^{-a x} + B e^{-b x} = \frac{A+B}{2}. However, if that's not possible, I'm wondering whether...