Exponential Definition and 1000 Threads

What I know: L = T - V V = e^(x1-x2) + e^(x2-x3) for n = 3 and a mass = 1 What I believe: T = .5Ʃ (x'_i)^2 from 1 to n So let's say you have three bodys that can just be considered pints masses of 1 and on the same line: x1 x2 x3 They have an...

Good day! I am reading the paper of Marc Yor (www.jstor.org/stable/1427477). equation (1.a) seems unfamiliar to me since the $ds$ comes first before the exponential part; $$ \int_0^t ds \exp(aB_s + bs). $$ Can you please help me clarify if there is a difference with the above notation as...

Homework Statement What is the greatest common divisor and least common multiple of the integers below (answer should be left in exponential form)? 2^{3}, 3^{3}, 5^{1}, 11^{2}, 13^{3} and 2^{1}3^{3}5^{2}7^{4}13^{1}Homework Equations The Attempt at a Solution This is exactly the way the...

Homework Statement Before the AP exam Cal Q Luss has 3 hours to cram: during this time, he wants to memorize a set of 60 derivative/integral formulas. According to psychologists, the rate at which a person can memorize a set of facts is proportional to the number of facts remaining to be...

Let X_1, X_2 \sim Exp(\mu) and Y = min(X_1, X_2) then find E[Y]. My attempt is as follows: $$E[Y] = E[Y/X_1<X_2]P(X_1<X_2) + E[Y/X_1>X_2]P(X_1>X_2) \\ = \frac{1}{2} (E[X_1/X_1<X_2] + E[X_2/X_1>X_2] ) \\ = \frac{1}{2} (1/\mu + 1/\mu) \\ = 1/\mu$$ But, we know that minimum of two exponentially...

The formula f(t) = I(1 + r)t gives the value of something after it has grown for t years, at rate r, with an initial value I. What if the growth rate r is continuously increasing? What is the formula now? Does it relate somehow to xx?

Hey, thanks for taking the time to look ay my post (: I have attached a file which shows the question I am stuck on, and my attempt at working it out. My problem is the answer I get, is different to what my Lecturer gets (shown in the attachment). He worked it out a different way to me, he...

Our textbook defines an exponential function as f(x) = ab^x. However, a question was brought up about a function, g(x) = 5^sqrt(x). Is g an exponential function? It looks like an exponential graph for x>0, but is not continuous on R. Thanks in advance!

I'm trying to find a function which will assign exponential weights depending upon sample size. nu=an equally space coefficient sequence (.05,..,.5; by=.05). m=sample size (10 in this case) Adding each observation in nu, implies a weight of 1, which makes the sum of weights m. I need...

Homework Statement Hi! I'm trying to find the PDF of W = abs(X-λ), where X is an exponential R.V. with rate parameter λ>0. Homework Equations The PDF for an exponential distribution is ∫λe^(-λx)dx. Taking the derivative of a CDF will yield the PDF for that function (I'm aware there are...

Simplify 8p-3 x (4p2)-2/p-5. This is what I got: First thing I did was flip everything to get rid of the negative exponents: p5/8p3x(4p2)2 next thing I did was multiply the 4p2 by 2 p5/ 8p3x16p4Then I subtracted thep5 from the 8p3 p2/8x16p4 and ended up with 1/128p2 I know that the...

Given that a random variable X follows an Exponential Distribution with paramater β, how would you prove the memoryless property? That is, that P(X ≤ a + b|X > a) = P(X ≤ b) The only step I can really think of doing is rewriting the left side as [P((X ≤ a + b) ^ (X > a))]/P(X > a). Where...

Show that $$ \lim_{n \to \infty} \prod_{1 \le k \le n}\left(1+\frac{kx}{n^2}\right) = e^{x/2}$$

Hi I have come across this equation: zn-1=\bar{z}, z\inℂ* (ℂ*:=ℂ\0ℂ) There are numerous obvious equalities that can be used, but I don't seem to reach a satisfying final answer. Any help would be appriciated. Thanks in advance :)

Easy exponential question---> 1/3(8)^(-2/3) Homework Statement I am doing a linear approximation question, and got stuck here with this simple stuff. 1/3(8)^(-2/3) Can anyone explain what I need to do to turn the above into 1/12 ? Homework Equations The Attempt at a...

1. Homework Statement - multiplication of trigonometric function and complex exponential 2. Homework Equations the question is, Akcos(ωt) × e-jωt 3. The Attempt at a Solution it is, Ak/2 + (Ak/2)e-j2ωt ? by using cos(ωt) = 1/2ejωt + 1/2e-jωt

Homework Statement (5 + √24)x + (5 - √24)x > 98 Homework Equations inequalities exponential The Attempt at a Solution I don't know how to start...trying to put log to both sides could not take me anywhere because the LHS can't be simplified...

Is there a reason why e doesn't have units attached? I've kind of just accepted it but was wondering the reason behind it.

How can we say: f(x)=A'sin(kx)+B'cos(kx) or equivalently f(x)=Ae^{ikx}+Be^{-ikx}?? How are these two equivalent knowing that e^{ix}=cosx+isinx I don't get this?

Hi, Somebody asked me for some help with his calc II homework, and this was one of the questions: "A hydra is a small freshwater animal and studies have shown that its probability of dying does not increase with the passage of time. The lack of influence of age on mortality rates for this...

Homework Statement Hi, I would like to get feedback if my z-plot is accurate for the following complex exponentiala: a=2*exp(j*∏*t) b=2*exp(j*∏*-1.25) c=1*exp(j*∏*t) d=-j*exp(j*∏*t) Further analysis: a= -2 because cos(∏) = -1 and sin(∏)=0 b= actual complex number A*cos(∅)+j*sin(∅) c= -1...

Homework Statement Determine the lowest derivative order for which the limit towards 0+ of the nth order derivative of f is nonzero (or otherwise does not exist). f = e^{\frac{-1}{x^{2}}} Homework Equations lim_{x\rightarrow0+}\frac{d^{n}}{dx^{n}}e^{\frac{-1}{x^{2}}} The Attempt at...

Hi, I have an equation with one unknown. This is the 'B' in the equation. I need to solve for 'B'. Can you help me to rearrange this complex equation to solve for B in terms of everything else please? =(() - (DCRMgAl)) ∗ ^(−∗(()+()))+ ((DCRMgAl )- (DCRAl ))∗ ^(−∗∗() )+((Al) - (DCRMg)) ∗...

Homework Statement Suppose that e^a=10 and e^b=4. Find the value of loga(b) Homework Equations ln(b)=loga(b)/loga(e) The Attempt at a Solution So far I've only gotten to the above equation rearranged to: ln(b) loga(e)=loga(b)/. I'm unsure as to where I'm supposed to go...

Homework Statement When a camera flashes, the batteries begin recharging the flash capacitor which stores the charge Q according to the function Q(t) = Q* (1-e-t/a) where t is the elapsed time in seconds since the camera flash and Q* and a are non-zero (a) What does Q* represent? (b) Find the...

Homework Statement Im not sure what each of the variables do in y=cax-p +q Homework Equations The Attempt at a Solution my understanding is that -q is for vertical shifts/transformations -p is for horizontal shifts/transformations -and c is for vertical stretching not...

I'm having trouble understanding the exponential map for nonlinear vector fields. If dσ/dt=X(σ) for vector field X, then how does one interpret the solution: σ(t)=exp[tX]σ(0) ? If X is nonlinear, then X is not a matrix, so this expression wouldn't make sense. If X is a...

How do you divide using ln: my example is x(7ln5-ln3)=-2ln5 and divide 7ln5-ln3 by both side to get x. So I have -2ln5/7ln5-ln3 and I can't seem to find the answer.

Homework Statement dy/dθ =2·3^(−θ) Homework Equations The Attempt at a Solution 2*(d/dθ)(3^(-θ) 2(3^(-θ)ln(3)) (2ln(3))/(3^θ) I keep getting this wrong and I'm not sure why. Could someone point out my mistake?

First-Order Linear System Transient Response Hey there, I am trying to solve a problem of first order equation which is A temperature sensor has a first order response with τ = 18 seconds. The calibration curve of the sensor is presented in Figure 1. Graph the sensor response when it is...

Homework Statement Hi, This is probably an easy equation and I know this is the pre-cal section and this is for my engineering math class but I feel like people in a pre-cal forum should be able to help! I'm writing an essay for my engineering math class and I am trying to calculate the income...

Homework Statement I just need some kind of explanation in layman's terms of what exactly is going on here. It seems as though I am missing some key element from trig. I am in a Signals class and the book lacks an explanation of the reduction used and ultimately why. Homework...

Dear PF users What is the rationale for Sze to write the exponential terms in ch. 1, Eq. 38 once as \exp \left[ -\frac{E_C - E_F}{kT} \right] and once as \exp \left[ \frac{E_F - E_D}{kT} \right] ? In both cases E_F is larger than either E_C or E_D. To me, for the sake of not having to worry...

I'm trying to understand the concept of exponential decay. To clarify, the decay of Uranium is not the same as say pulling the plug in a tub full of water. The water will drain out of a tub at a steady rate from start to finish. I assume Uranium doesn't do that. So you COULD say the water has a...

The derivative of e^(2x): let y = e^(2x), let u = 2x, so y = e^u chain rule: du/dx * dy/du = 2*e^u = 2e^u = 2e^(2x) this is the solution copied from my book, my question is why do they let u = 2x? is e^u the same as e^x? If so then wouldn't all derivatives of the exponential functions be in...

Hi guys I'm helping my girlfriend with her Calc 1 homework and we seem to be stuck on this one problem. Am I missing something obvious? Homework Statement Homework Equations P = P_0 a^t \frac{5}{20} = \frac{P_0 a^1}{P_0 a^{-1}} \frac{1}{4} = a^2 a =...

Hello forum, I recently lost my notes on this matter, so I hope someone can fill in the gaps in my memory. The problem I am working on is the following: For one ticket window, the waiting time for one people satisfies an exponential distribution λe-λt and expected waiting time is 4 min...

WHY!? is the relationship between speed and time exponential? I am actually a finance major but I like to learn about physics on my spare time. One of the more fundamental concepts I am having a hard time understanding is why the relationship between speed and time is exponential. Can someone...

Hi there, I learn from the text that the exponential of an operator could be expanded with a series such that e^{\hat{A}} = \sum_{n=0}^{\infty} \frac{\hat{A}^n}{n!} So if the eigenvalue of the operator \hat{A} is given as a_i e^{\hat{A}}|\psi\rangle will be a matrix with diagonal elements...

Homework Statement A radioactive substance diminishes at a rate proportional to the amount present (since all atoms have equal probability of disintegrating, ...). If A(t) is the amount at time t, this means that A'(t)= p * A(t) for some p representing the probability that an atom will...

I am reading the about the derivative of an exponential function using the limit definition, but one step I don't quite understand: lim_{h\rightarrow0}\frac{a^h -1}{h} = f'(0) Wouldn't that limit equal 0/0?

How does the given equation: βe^(x/β)-x = β+(A/B) solves to x = √(2A/βB) when β is large?

For an exponential function of the form y=a^x First derivative , d/dx [a^x ] = a^x∙ lim┬(δx→0)⁡{(a^δx-a^0)/δx} = a^x∙ m_((0,1)) now if m_((0,1)) which is the gradient of the y-axis intersection point of the exponential function equal to 1 exactly...

if first derivative is the slop of the given functions, then what is the physical meaning of exponential function remaining the same function after differentiation?? does it mean its vertical tangency make it indifferentiable? please clarify me the concept... regards

Homework Statement (4x)^(1 + log(base 2) (x)) = 8(x^3) What is the sum of the values of x that fullfill that equation? A) 2.5 B) 2.0 C) 1.5 D) 1.0 E) 0.5Homework Equations Use the exponential equation only and make the lower one (exponented) 1.The Attempt at a Solution (4x) = (2 x^(1/2))^2...

Homework Statement When attempting to divide the following equality (a "tangency condition" in microeconomic consumer theory), I'm puzzled by the solution derived here, please explain the procedure for arriving at the solution. Many thanks! Homework Equations I differentiated the...

Hello, I'm having hard times with the following simple linear ODE coming from a control problem: $$u(t)' \leq \alpha(t) - u(t)\,,\quad u(0) = u_0 > 0$$ with a given smooth α(t) satisfying $$0 \leq \alpha(t) \leq u(t) \quad\mbox{for all } t\geq 0.$$ My intuition is that $$\lim_{t\to\infty}...

How does the exponential function work

So I have a situation where the results in a table (x and y), where y reaches 0. According to my understanding, mathematically, exponential decay can never reach 0, right? So does that mean that I can't use an exponential curve of best fit with the results in my table (x = 0,1,2,3), (y = 4...

You are given a random exponential variable X: f(x) = λ exp(-λ x). Suppose that X = Y + Z, where Y is the integral part of X and Z is the fractional part of X: Y = IP(X), Z = FP(X). Which is the following conditional probability: P(Z < z | Y = n) for 0 ≤ z < 1 and n = 0, 1, … ?