E^x Definition and 129 Threads

Find the Taylor polynomial of degree 9 of f(x) = e^x about x=0 and hence approximate the value of e. Estimate the error in the approximation. I have written the taylor polynomial and evaluated for x=1 to give an approximation of e. Its just the error that is confusing me. I have: R_n(x) =...

[SOLVED] Re: Integral involving square root of e^x Homework Statement \int \sqrt{1-e^{-x}} Homework Equations Sub rule. The Attempt at a Solution I realized that it's fairly obvious I can use u=e^-x/2 to give \sqrt {1-u^2} but I'm kind of looking at the answers and I'm not seeing how I...

Homework Statement Integrate from e^x to e^2x: (sin^2(t) + cos^2(t) -1)dt Homework Equations just standard integral equations The Attempt at a Solution I know how to do most of it, my only question is: is (sin^2(e^2x) + cos^2(e^x) -1) a special trig identity? or would i just...

the quesion is below, show that show that ( 1+ \frac{x}{n} ) ^n < e^x at the first, i take log on both sides,.. but i couldn't go further. can someboday help me? thx

I must be brain dead ,but I can not seem to compute the derivative of e^x/sqrt2 I am stuck when I used the quotient rule for derivatives

please explain in more detail on how we come up with the answers below. Thanks in advance! (formulas much appreciated) Differentiate: 1. y=e^x =e^x 2. y=lnx =1/x

How can I solve: (x^2)(e^x) - e^x = 0 and 2e^(2+x)=6 For the first one, tell me if this is right: e^x(x^2-1)=0 -> e^x = 0 and x^2 - 1 = 0 so x = 1 and 0? but 0 doesn't work when I plug it back in. so is 1 the solution for x?

Homework Statement For which real numbers c is (e^x+e^{-x})/2 \leq e^{cx^2} for all real x? Homework Equations The Attempt at a Solution I think you can expand both sides into series and term by term compare them. The left side is \sum_{n=0}^{\infty}\frac{x^{2n}}{2n!} Can...

Is it possible to intergrate e^x (cosx) i wondered because i tried to intergrate it by parts, but ended up going round in circles. I wondered because i had this question and I am stuck on how to do it :) http://img505.imageshack.us/img505/320/frfbc8.png

Homework Statement I want to solve for the derivative of e^x using the limit definition. Homework Equations http://www.math.hmc.edu/calculus/tutorials/limit_definition/img10.png The Attempt at a Solution obviously the derivative of e^x is itself, so i konw the answer. i just...

how would i prove that e^x >= 1 + x for all x in [0,inf)?

I am a little stuck how to solve this equation e^x = 5-2x? I did ln e^x = ln (5-2x) x = ln(5-2x) / ln e but iam not sure how to bring the other x around to the side with the x to solve the equation?

How does one integrate \int_{}^{} \frac{e^x}{x}dx I could expand it using a Laurent series and than integrating term by term but are there more elementary methods?

i need to prove that: 1+x+x^2/2!+...+x^n/n!<=e^x<=1+x+x^2/2!+...+x^n/n!+(e^x)x^(n+1)/(n+1)! for x>=0 without using the power sum of e^x. the textbook hints that i should evaluate the integral \int_{0}^{x}e^udu and then i should integrate over and over n times, and obtain the upper and...

integ [e^x / (1 + e^2x ) ]dx.can someone show me how to solve this by using 1 / (1 + x^2 ) formula?? pls...

Hi I'm having some trouble with evaluating these limits. I can't figure out what to do. I guess i forgot some calc one. I don't have much work but All I'm asking for for now is a couple hints. \lim_{x\rightarrow\infty} \frac{e^{3x} -e^{-3x}}{e^{3x} + e^{-3x}} I tried dividing numerator and...

Hi, I'm trying to solve this: Find all general maximum solutions of this equation y'(2-e^{x}) = -3e^{x}\sin y\cos y First, there are some singular solutions: If y \equiv k\frac{\pi}{2} Then right side is zeroed and so is the left. To convert it to the separate form, I need to divide...

why does d e^x / dx = e^x ?

just starting up the school year again and my brain is not there yet. Is e^x an even or odd function. also what about e^x + e^-x and e^x - e^-x thanks for the help.

Hey, everyone I am working on a calc problem, and I have no idea where to start. The integral is e^x ------------- [division problem] (25+e^2x)^4 Do I let my u equal to the 25+e^2x? or what... then after that what do i do. Thanks for all the help in advance. -Eiano

hi , 1.)how do I find the limit of (x! e^x) / (x^x *x^1/2) as x tends to infinity ? 2.)and is f(x)= x! a function ? if so, how do I find the derivative ? thanks for any help Roger

hi, i have a question. :rolleyes: e^x =0 is this possible, and for what values of x if so.?

Hi all, I've been having little problems getting Fourier series of e^x. I have given f(x) = e^{x}, x \in [-\pi, \pi) Then a_0 = \frac{1}{\pi}\int_{-\pi}^{\pi} e^{x}\ dx = \frac{2\sinh \pi}{\pi} a_{n} = \frac{1}{\pi}\int_{-\pi}^{\pi} e^{x}\cos (nx)\ dx =...

Ok, here is the integral i seem to be having some issues with. I know there's a very simple step I am missing. \int_{}^{} e^x \sin(\pi x) dx i attempted to do this using by parts integration. I tried u = \sin(\pi x) so du= \pi \cos(\pi x) dx so then dv= e^x dx and v= e^x...

I don't understand why the derivative of e^x is e^x itself.

Some one please show me how to do this problem below Integral of e^x cos(x) dx how to I integrate that? thanks

The text wants me to find x using a graph, but since I don't like taking my sweet time building one so accurate to find an answer to one decimal place, I rather find x without the graph. This is it: e^x = x^10 This isn't important or anything, but I figured that I can use some practice...

I had a question on a math test which said that you should find an approximation for e^x which is very good for x \approx 0 . First I declared the function f(x) = e^x . We have the interesting thing that f(x) = f'(x) = f''(x) = f'''(x) \ldots \ \forall x . And because of this we have f(0)...

I'm revising over my maths for my exams and I just came across something I didn't understand. How do we know that: \frac{d}{dx} \left( e^x \right) = e^x I've seen the infinite series for e^x but in our maths class we derived it by assuming the above statement :confused:. Preemptive thanks...