Exponential function Definition and 166 Threads

Dear All, I am searching for an upper bound of exponential function (or sum of experiential functions): 1) \exp(x)\leq f(x) or: 2) \sum_{i=1}^n \exp(x_i) \leq f(x_1,\cdots,x_n, n) . Since exponential function is convex, it is not possible to use Jenssen's inequality to get an upper bound...

Homework Statement Given that Q=Pa^t and Q doubles between t and t+d, prove that d is the same for all t. Homework Equations Q=pa^t The Attempt at a Solution This is what I've tried so far: Q_0=Pa^t and Q_1=Pa^{t+d} Then: \frac{a^{t+d}}{a^t}} \equiv 2 This is where I begin drawing blanks...

Homework Statement Express b^{x} as a function of logarithms. Homework Equations There are a couple of equations in the attempted solution. I can't say if they are actually relevant The Attempt at a Solution I've investigated the property y = log_{b}(b^{y}), and also...

good evening all! Homework Statement Determine the exact values of j^j Homework Equations j = sauare root of -1 The Attempt at a Solution stuck :cry: :cry: :cry:

Homework Statement find y', y = \frac{e^x}{1+e^x}Homework Equations derivative of e^x = e^x, quotient rule.The Attempt at a Solution The old man is back, sorry, and I don't seem to be able to enter this using the tex stuff. This is from Kline's Calculus, page 348. I proceed as follows: y' =...

I am trying to find the polar notation for 1 + e^(j4) I know that e^(jx) = cos x + jsin x = cos(4) + jsin(4) I can then find the magnitude and angle. This is nowhere close to the answers below. 1) cos(2) + 1 2) e^(j2)[2cos(2)] 3) e^(-j4)sin(2) 4)...

Hey, I have a problem involving natural logs which has got me confused, even though it appears simple. The problem: Find the exact coordinates of the point on y = e^x where the gradient is 2. From previous experience, I know that differentiation is required, but because of the e I am not sure...

find the intervals of increase and decrease of f(x) = e3x + e-2x. f'(x) = 3e3x - 2e-2x I set f'(x) = 0 to find the critical numbers: 3e3x = 2e-2x 3 ln e3x = 2 ln e-2x 9x = -4x x = 0, which is obviously wrong, (3e^0 - 2e^0 = 1). I found out that I had to combine the two terms using a...

Hi there, I have googled for the R square formula, but it's very confusing, so I need some help. Please come up with an example on how to use it, if I have a exponential function on how i want to calculate its R square. Thanks:cry:

I am trying to solve this Fourier problem where I have to integrate ∫f(x) * exp(-i§x) dx from -∞ to ∞ , where f(x) = exp(-sgn(x)) I tried breaking the function into two pieces where x is from -∞ to 0 and from 0 to ∞ where f(x) would then be exp(x) and exp(-x) and integrating two functions...

Hi, I'm working on this: Given that \lim_{n \to \infty} \psi(n)=0 and that b and c do not depend upon n, prove that: \lim_{n\to \infty}\left[ 1+\frac{b}{n} +\frac{\psi(n)}{n}\right]^{cn} = \lim_{n\to\infty} \left(1+\frac{b}{n}\right)^{cn}=e^{bc} So far, I've taken the natural log of both...

i'm having problems with two questions. Please help me! Thanks! I've tried everything but i can't solve them... :confused: :frown: 1) Solve: (3/4)^3x-2 * (4/3)^1-x = 9/16 2) Solve for x : 3(3^x) + 9(3^-x)=28

help me to solve this problem find exponential function f(x)=Ca^x with the 2 given points (0,5)(2,5/9)

algebra 2 help...need it desperately does anyone know algebra 2, i need to know how to complete this equation... an expotential function of the form y=a(2)^x passes through the point (3,4). Find the value of a. choices a)2 b)1/2 c)3 d)3/4

Hi, I am having a bit of trouble, i am getting ready for an exam, one the questions i have asks "given the curve y = e^x, draw tangents to esitmate the gradients of the curve when a)x=0, b)x=1, c)x=-1, Now i know the answers are: a) 1 b) 7.39 c)0.05 However the toruble i am...

Just to lighten up a little: A Constant Function and an Exponential Function are walking through the forest. Suddenly, through the dense bushes, they see a Derivative walking around. The Constant Function hurries to hide behind a tree in anxiety. Exponential: "What's wrong?" Constant: "If...