Exponential Definition and 1000 Threads

Homework Statement problem 1 diff([f(tanx)], x) = x^2; prove that diff[f(u)]=(tan^-1(u))^2/(1+u^2) problem 2 int(f(u), u = 0 .. 1) = f(t)-1; prove that f(a+b)=f(a)f(b) for every a,b ∈R The Attempt at a Solution problem 1 i don't know how to answer this...

I am learning calculus from a book of mine, and it gave an example problem of exponential growth (as derived from the exponential differential equation of dy/dx = ky to be y=Ce^kt) saying a population is growing at a rate of 2% per year, and says that K, the growth constant, in this case is k =...

Homework Statement I don't understand why they took M(e)=1 , and how the proceed on with the proof. Thanks in advance(= Homework Equations The Attempt at a Solution

f(x) = 2^x \left \left f(kx) = 2^(kx) \left \left b = 2^k \left \left b^x = 2^(kx) \left \left b^x = f(kx) \frac{d}{dx}(b^x) = \frac{d}{dx}(f(kx)) = \frac{d}{dx}(2^(kx)) (1) \frac{d}{dx}(f(kx)) = k.f'(kx) (2) I can't see how step (1) gets to step (2). Because I thought...

Homework Statement Hi all Is infinity a minimum of the exponential function f(x)=ex or not? I personally do not think so since it is a limit, but I wanted to ask you guys to be 100% sure.

Are there any general methods to solve the following complex exponential polynomial without relying on numerical methods? I want to find all possible solutions, not just a single solution. e^(j*m*\theta1) + e^(j*m*\theta2)+e^(j*m*\theta3) + e^(j*m*\theta4) + e^(j*m*\theta5) = 0 where...

Homework Statement \frac { d^2 \theta }{d x'^2 } = -y *exp(\theta) eq. 1 mayb be integrated to yield exp(\theta) = \frac {a}{cosh^2(b \frac{+}{-} \sqrt \frac{a*y}{2} * x')} \theta = f(y,x') Homework Equations The Attempt at a Solution the exponent is throwing me off, but i probably...

Let X1, X2, ...Xn be independent exponential variables having a common parameter gamma. Determine the distribution of min(X1,X2, ...Xn). The Attempt at a Solution I know how to do it with one X and one parameter but I am at a loss with these multiple ones... Thanks so much!

Homework Statement -Find the intervals on which f is increasing or decreasing -Find the local maximum and minimum values of f -Find the intervals of concavity and the inflection points f(x)=xex f'(x)= ex+xex then I must solve for x when the function equals zero to find my critical numbers...

I have been given a Indice. I've been trying to figure it out for awhile and need some assistance, It'd be great if someone could work it out and show me the steps they did and even explain it. ([a-2b-3/ 2a3b-4]2 )/ [ab-15]/a-3b2]) I've attempted the working out in my book, Its abit hard...

Hello all, I am trying to solve an integral with Mathematica, but I do not succeed. I am wondering whether the integral cannot be solved, or whether Mathematica cannot solve the integral, or whether I am doing something wrong. Details: * Mathematica does not seem to be able to solve the...

Homework Statement y=9-x Homework Equations The Attempt at a Solution dy/dx=-9-xln9 We are provided with the answers. I do not understand the concept behind how to get from the question to the solution. What rule(s) are applied? If somebody could solve this single question...

Homework Statement i have to integrate e^(-y) / y and i found out that you have to use this exponential integral and someone else said it doesn't have an integral. either way I am thoroughly confused The Attempt at a Solution i have no clue what so ever. The original question had it in...

Homework Statement lim e3/(2-x) x->2+ The Attempt at a Solution I can't seem to get started on this one.

Homework Statement The bus service operates between points A and B. The buses depart from the terminal station A with headways that follow the negative exponentioal distributiona with parameter 10 trips per hour. Assume that the characteristics of the system remain the same over time (not...

Hi all, I'm trying to solve the definite integral between 0 and inf of: exp(a*x^2 + b*x + c) --------------------- dx 1 + exp(m*x + n) with a,b,c,m,n real numbers and a < 0 (negative number so it converges). I've read in the forum's rules that I have to post the work that I have...

Homework Statement - A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 63 cells. - (a) Find the relative growth rate. Homework...

Homework Statement y = x^(18x^-4) Homework Equations chain rule dy/dx a^x = a^x ln a The Attempt at a Solution first i used the second equation from above to get x^(18/x^4)*ln(x) then i use the chain rule to get x^(18/x^4)*ln(x)*(-72x^-5) the computer program i am using is...

Solving Exponential Equations SO CONFUSED ? Homework Statement I'm trying to solve problems like these a) 2(3y-2) = 18 b) 27(33x+1) = 3 c) 2x+2 - 2x = 48 d) 10z+4 + 10z+3 = 11 Homework Equations Laws of exponential values. The Attempt at a Solution b) 2(3y-2) = 18 6y-2 = 18...

Is there an approximation for exp(-k*L) with L large but finite??

Hi, I have a (markov chain) transition matrix X which I understand. In particular each row of this matrix sums to 1. I have used this transition matrix to construct it's generator, Y. I.e. Y is the continuously compounded transition matrix, X = exp(Y) X*X = exp(2Y), etc both X and Y...

I'm trying to find the laplace transform (if possible) of exp(-2r/a)r^2. --- I did integration by parts to check that the integral of exp(-2r/a)r^2 from 0 to infinity is a^3 / 4. but i cannot get the laplace transform to work out. the answer mathematica online gives would have to have the term...

Homework Statement how can i convert this : - 2 (cos pai / 4 + i sin pai / 4 ) to Cartesian , Polar and Exponential form ? Homework Equations z = ( a + i b) The Attempt at a Solution r= -2 tan inverse = pai/4 / pai/4 ?? Thank you very much for helping me out

Express -2(cos pai/4+i sin pai/4 ) in Cartesian , Polar and Exponential form ? how can i convert this : - 2 (cos pai / 4 + i sin pai / 4 ) to Cartesian , Polar and Exponential form ? Thank you very much

I want to solve a first order differential equation on the form y'+y=e^{x} I want to separate the variables, but not sure how...Thanks!

I have a problem with an exponential function. I am wondering if an exact solution is possible, or if I have to write the solution as a logarithm of an unknown. A formula says that E(z)=E(0)^{-kz}, where E is light intensity and z is depth in water. My objective is to find the constant k. I...

I am having trouble solving this problem. I'm not sure how to solve this problem... Assume X and Y are independent exponential random variables with means 1/x and 1/y, respectively. If Z=min(X,Y): Is Z exponentially distributed as well (if so, how do you know)? What is the expectation of Z...

Homework Statement for x and y satisfying x-y=2 and 2^{x}-2^{y}=6 find 2^{x}+2^{y}. The Attempt at a Solution x-y=2 ; x=2+y log_{2} 2^{x}-log_{2}2^{y}=log_{2}6 log 6/log2=2.585 x-y=2.585 but this violates the intitial condition x-y=2 where am i going wrong?

I feel like I'm doing everything correctly but my answer for (b) doesn't make any sense. Assume that bacteria in aculture grows according to an exponential growth model. If the number of bacteria grows from 50 to 1000 in 12 hours: a)How many bacteria will be present after 18 hours? b)How...

hey I am doing some questions outta a txt book, i sort of understand complex numbers, like multiplying and dividing, .. The question asks to rearrange for z, e^(iz) = i - 1 im not sure what to do with the exponential function. thanks for the help

Homework Statement 10(1 + e-x)-1=3 Homework Equations The Attempt at a Solution I'm supposed to solve for x, but I don't know how to go about this. I tried dividing the 3 by the 10, but after that I don't know what to do. I believe I should use ln on both side, but that's after...

Homework Statement Show that \overline{e^{i\theta}} = e^{-i\theta} Homework Equations The Attempt at a Solution So I what's going through my mind is that the problem above is pretty much the same as saying \bar{z} = z^{-1} Then to prove it is all I need to say is that...

Homework Statement e^{i\theta_1}e^{i\theta_2} = e^{i(\theta_1 + \theta_2)}}Homework Equations The Attempt at a Solution For some reason every I multiply (cos\theta_1 + isin\theta_1)(cos\theta_2 + isin\theta_2) I am getting (cos\theta_1 cos\theta_2 + sin\theta_1 sin\theta_2) + i(sin\theta_1...

Homework Statement I was studying L'Hopital's rule and how to deal with indeterminate forms of the type 0^0. It's not clear to me how lim e^f(x) = e^lim f(x). In wikipedia http://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rule" (under other indeterminate forms) it says "It is valid...

Hello, I am trying to find an analytic solution to the following: \int_{-1}^{1}\exp(-p\sqrt{1-x^{2}}-qx)dx where p,q > 0. Does anyone have any ideas? Thanks.

Homework Statement This topic is under linear system differential equation.Solve the system by using exponential method. Just want to ask the expansion of exponential function Homework Equations e^x=1+x+(x^2)/2!+(x^3)/3!+... The Attempt at a Solution then how about the e^(-x)=...

Homework Statement This topic is under linear system differential equation.Solve the system by using exponential method. Just want to ask the expansion of exponential function Homework Equations e^x=1+x+(x^2)/2!+(x^3)/3!+... The Attempt at a Solution then how about the e^(-1)=...

1. I need to solve the following exponential equation for t. \frac{1}{20} =0.5 e^{-0.877t} - 0.05 e ^{-9.123t}

I haven't been taking math for 3 years so I have a question about the following: is 14m6n2 the same as 2mn x 7m5n basically asking this because I am not sure whether or not I can factor the terms out like this if this information is insufficient I can post the whole problem. Thanks in advance.

Will anyone help me to find out the analytic expression of the following 2^N\times2^N exponential? exp[t(X\otimes X\otimes I\ldots\otimes I+I\otimes X\otimes X\otimes I\ldots\otimes I+\ldots+I\otimes I\otimes\ldots I \otimes X \otimes X+X\otimes I\ldots I\otimes X)], where...

Homework Statement I'm unable to integrate the following function with respect to x [-inf, +inf]: Homework Equations exp(y*x)*(1+exp(x))^(-n)dx The Attempt at a Solution I tried to expand the function by distributing the exponent (-n) across the rightmost product, but I don't think its...

it is suspected that cells in a sample are dividing so that the number of cells present at anyone time t (measured in seconds) is growing exponentially according to the relationship y = 64 x 2^2t. it would be hard to check this relationship accurately by plotting measurements of y against t, so...

Hey everyone, I'm new to using the Maxima software and I'm having some trouble. When I enter the following formula to be evaluated: diff(1-exp^(-t/R*C),t); I get the following output: \frac{log\left( exp\right) \,C}{{exp}^{\frac{t\,C}{R}}\,R} This doesn't look right, even if I...

Hello, I've been solving a problem which forces me to answer the question: "Is there a boolean function with exponential number (in variable count) of prime implicants of the length n - 1?" Anyway, during solving this problem I came to this point: Is the following sum exponential in 2n...

I am trying to read through this paper on the standard model. The ideas seem straightforward enough, but as always, I'm tripping over the "physicist's math" it uses. I was wondering if I can get some clarification or general guidance...

Homework Statement Solve the exponential equation. 1. (22x)+(2x) - 12 = 0 2. 3 * 4x + 4 * 2x + 8 = 0 Homework Equations The Attempt at a Solution 1. 2x ln 2 + x ln 2 = ln 12 x(2 ln 2 + ln 2)= ln 12 x=( ln 12) / (2 ln 4). I'm thinking I'm factoring out the X...

J.J. Sakurai Modern Quantum Mechanics p. 74 It says, [A,H] = 0; H|a'> = Ea' |a'> where H is the Hamiltonian A is any observable |a'> is eigenket of A then, exp ( -iHt/h)|a'> = exp (-iEa't/h)|a'> where h is the reduced Planck's constant. I want to know WHY ? and besides, I would...

Hello, Suppose that: Z=X_1+X_2+X_1X_2 where X_i for i=1 and 2 are independent and identically distribuited exponential RVs. can we find the PDF of Z? Regards

As a kid, I remember my father saying "there's a small chance that an electron in your body is on the moon" Well, today I decided to calculate the odds. Among the assumptions I made to make math easier. *Ground state wave function of Hydrogen *the moon is a cube of sides 2r. where r is...

Homework Statement An investment pays 8% interest, compounded annually. a) Write an equation that expresses the amount, A, of the investment as a function of time, t, in years. b) Determine how long it will take for this investment to 1. Double in value, and 2. Triple in value. c) Determine...