E^x Definition and 129 Threads

Homework Statement I'm just not sure what the answer to this is. I think it's an identity for e^x and ln, but I've never had a course that dealt with e^x or logs. So I don't know. What is the answer to e^14ln(x)? It's part of a larger problem, but I can't get the rest of it done until I...

Homework Statement this is definite integral question. lower limit 0 ; upper limit 1 ; integral (e^x)(x-1)^n = 16-6e find n (n<6) here e is euler constant value around 2.7 (irrational) hope you understood. Homework Equations as much as first year student know. The Attempt at a Solution...

i'm battling unsuccessfully to find a delta epsilon proof for continuity of exponential function. this is what I've tried so far but its failed either because I've gone down a blind alley or got stuck on the right path I'm not sure which one: find lim e^x x->a therefore...

Find the general solution to: dy/dx = ex+y Im not sure if I am doing this right or not. i tried saying ex+y = ex x ey and using partial differentiation to solve it but keep getting the same as the question: ex+y i know differentiating ex gives ex so is it the same in this case?

Homework Statement Find E[e^x] where x~N(\mu, sigma squared)Homework Equations The Attempt at a Solution It looks like a moment generating function. Here is what I did: Assume X= \mu + \sigma*Z E[etx]= E[et(\mu+\sigma*Z)] I simplified it and used the fact of moment generating functions...

Homework Statement prove that e^x > sigma from i= o to n (x^i/i!) for every x>0 Homework Equations The Attempt at a Solution I will do it by induction for n=1 e^x > x+1 but e^0=1 and 0+1=1 f(x)=e^x , g(x)=x+1 f(0)=g(0) f'(x)=e^x , g'(x)=1 e^x>1 for every x >0 so...

Homework Statement The question reads very simply, show that ex \geq1+x \forall x > 0Homework Equations None to speak of. I am not allowed to use calculus, and this is why I am having problems. The Attempt at a Solution I tried to break it up into cases: When x=0, ex=e0=1 1+x=1+0=1 Hence...

Homework Statement find integral e^x ln(x)dx Homework Equations integral udv=uv-integral vdu The Attempt at a Solution u=ln(x) ,du=1/x dx dv=e^xdx ,v=e^x integral e^x ln(x)dx=ln(x)e^x -integral e^x/x dx integral e^x/x dx = u=e^x du=e^x dx , dv=1/x dx , v=ln(x)...

Homework Statement proving it Homework Equations The Attempt at a Solution from (-infinity , 0) x is <0 e^x >0 for if there exist an positive a such that e^x=-a then x =ln(-a) which is undefined therefore e^x>0>x in (-infinity , 0) from [0,infinity) since x+1>x we prove...

Homework Statement I tried expanding e^x and evaluated the limit as 1. The answer given is 0.

Homework Statement what is the derivative of e^[(-X^2-2x+1)/2] Homework Equations The Attempt at a Solution Is this right? = -(x+1)e^[(-x²-2x+1)]

Homework Statement Let f(x) = ex + ln x Find (f-1) ' (e) Homework Equations let y = f-1 x The Attempt at a Solution I tried finding the inverse of f(x) but got stuck. I arrived at: x = ey + ln y How do I make y the subject of formula?

Homework Statement Evaluate ∫ e^x dx upper limit: 3 ln2 lower limit: 0 Homework Equations The Attempt at a Solution I'm not sure if I'm doing this right; the integral of e^x = e^x now with the lmits [e^3ln2 - e^0] ? lol thanks

Homework Statement Plot e^x for -10 to 10 using a Taylor series about 0 find the error between the nth term and the actual value of e^-10 and e^10 plot sin(4*theta) using a 2 term expansion, a 4 term expansion and a 10 term expansion and constrast it with the plot of sin(4*theta) The Attempt...

Here is a different way I (think I) proved that the derivative of e^x is e^x:https://docs.google.com/document/edit?id=1_QqZaeDlQObgbTg3zd5ezlWuaUol92k7cBaOjdBzoSM&hl=en&authkey=CPuduaIB Are my "rules" with infinitives correct or do they not work in other cases?

Homework Statement Doing a DE and need to solve for y, just wondering about this particular case. Homework Equations ln ((2y-1)/(y-1)) = x for y The Attempt at a Solution Wolfram says the result is...

Hello As I was trying to figure out why the derivative of e^x = e^x using the derivative definition I faced this limit: lim (e^x - 1)/x ; x goes to 0 and I need your help, thank you.

Homework Statement Use the Maclaurin expansion of e^x to find the value of e correct to four decimal places. (This is not the same as simply using the first four terms of the expansion.) I did the question but i had to look up how many terms to use to be accurate to four decimal places (8)...

1. f(x)= ax^2 = ae^TR, nez Prove f '(x) = a(n) x^(n-1)2. n does not equal 03. I don't even understand it

Homework Statement I need to demonstrate that \frac{\mathrm{d} }{\mathrm{d} x}\sum_{n=0}^{\infty }\frac{x^{n}}{n!}= \sum_{n=0}^{\infty }\frac{x^{n}}{n!} Homework EquationsThe Attempt at a Solution I just need a hint on how to start this problem, so how would you guys start this problem?

Homework Statement Differentiate e^x * cotx / 5sqrtx^2 [Sorry for not using the formatting things. They didn't seem to be working for me, and this is urgent!] Homework Equations The quotient rule seems like that's the way to go... The Attempt at a Solution At first I tried using...

Homework Statement g(x)=ex and the x-axis on the interval [0,ln(9)] a) Set up definite integral that represents area b) Find area using fundamental theorem. Homework Equations The Attempt at a Solution g(x)=ex [0,ln(9)] \int^{ln(9)}_{0}e^x dx = [eln(9)]-[e0] = [9]-[1] = 8...

f'(x)=sin((pi (e^x)) /2) and f(0)=1 then f(2)= ? so i integrate and get -(1/((pi/2)*e^x)) cos((pi (e^x)) /2)+ 1=1 when i plug two into that i don't get any of the answers listed a)-1.819 b) -.843 c.) -.819 d) .157 e) 1.157

[sloved]Does anyone know how to find radius of convergence for sin x and e^x We know that to find radius of convergence we use ratio test (ie lim {a_n+1} /{a_n}) Can this method be used for sin x and e^x? ( whose radius of convergence is -infinity and infinity) if radius of convergence is...

The function y=e^x can be expanded using the power series, thus y=e^x=1+x+\frac{x^2}{2}+\frac{x^3}{3!}+... This is a polynomial of infinite degree, and the theorem that says a polynomial must have at least one root in the complex field, and thus this extends to a polynomial of nth degree having...

Can anyone help me ? I am completely lost on this one

What makes the Maclaurin series for e^x so amazing? My teacher was talking about how the Maclaurin series for e^x is one of the most amazing concepts in mathematics but he wasn't able to extrapolate due to a lack of time. Anyone care to explain why this particular series is to magnificent...

Homework Statement e^x = \frac {k}{c}sin^2(y) solving for t i thought it was t=arcsin(\sqrt{\frac{ce^x}{k}}) but my calc is saying like the answer above + ln4*pi + pi.

Homework Statement evaluate integral (0, 1) f(x)=e^x Homework Equations integral (a,b) f(x) dx = lim n-> infinity, sum of (i = 1, n) f(xi*)Deltax where : delta x = b-a/n xi*= a+(delta xi) The Attempt at a Solution Deltax= 1-0/n = 1/n xi*=0+(1/n)i = i/n f(xi*)Deltax =...

Okay, before you scream x = ∞, I'm finding the complex solution to the problem. I'll show you my working so far, maybe you'll see something I missed. First let x = a+bi e^(a+bi) = a+bi e^a * e^bi = a+bi Applying Euler's identity e^a*cos(b) + ie^a*sin(b) = a+bi e^a*cos(b) = a e^a*sin(b) = b...

Is there someone who can explain why this is true, or point me to an online resource that provides a proof of it? e^x = \lim_{n\to \infty} \left(1 + x/n \right) ^n I know that in some ways, this is how the exponential function is defined. But any resources you can provide that explain it...

Homework Statement Let r \in \mathbb{R}. Show that \lim_{x \to +\infty} x^r / e^x = 0 Homework Equations The Attempt at a Solution Intuitively, this is clear since exponential growth (i.e. denominator) is greater than linear growth (i.e. numerator). If r \in \mathbb{N} then it...

Homework Statement \int\frac{1+e^{x}}{1-e^{x}} dxHomework Equations .The Attempt at a Solution I've tried substituting for u=e^x or u=1-e^x but I can't seem to get anywhere. Haven't done calc in a while and just want someone to point me in the right direction. Thanks.

Homework Statement Integrate Sqrt[ ex+1] 2. The attempt at a solution I first multiplied the equation by e^x / e^x, then tried substitution, with u = e^x + 1 du = e^x dx This gave me: Integral 1/(u-1) * (u)^1/2 du However, I'm stumped at this part. Substitution here doesn't...

I've been studying calculus and have always been confused about the property of e^x. "e is the unique number such that e^x is equal to its derivative." I haven't ever really understood why, but have figured it would pop up some time later. Unfortunately, it still hasn't popped up, so I've...

Homework Statement Integrate -9e^x - 28 / e^2x + 9e^x + 14 It gives a hint which is substitute u = e^x. Homework Equations The Attempt at a Solution I want to integrate by partial fractions if possible... however before I can do that, I need to make the substitution, and I...

Homework Statement the value of f(x) = (sqrrt e^x +3) at x=0.08 obtained from the tangent to the graph at x=0 is...? Homework Equations The Attempt at a Solution i used linear approximation. (sqrrt e^o +3) + (1/2(sqrrt3+e^0)(0.08) i got an answer but i know its wrong. i...

Homework Statement Find the minimum distance from the origin to the curve y = e^x.Homework Equations Distance Formula The Attempt at a Solution http://carlodm.com/calc/prob6.jpg 5-6 bright Calculus kids in my high school grappled with this problem and we couldn't find an answer. Can...

Homework Statement Problem: Find the value of b for which Homework Equations Power series for (1/1+x) or in this case, power series for (1/1+b) The Attempt at a Solution I keep getting ln (-5/6) as the answer, but apparently the correct answer is ln (5/6). I do not see why...

In calc we are having like this flash card quiz and you have to apply things to the graph of like e^x or lnx. I was wondering how do you determine the domain range of graphs like these. for example e^x graph domain is all reals, and the range is 0 to infinity. How would you transform this...

Hi Could you please tell me how to integrate it? Thanks ~~ \int_{-\infty}^{\infty} \frac {e^{i\omega t}} {1+\frac{t^2}{\tau^2}} dt where i is imaginary unit, \omega, \tau are positive real,

I solved this problem a couple months ago, but seem to have forgotten some rules of calculus with regards to e in the meantime. The goal is to just solve this integral. Integral from 0 to +inf of (e^tx) times (5e^-5x) dx Now - in my work I got the answer of 5/5-t, which is correct. In the key...

I've been drawn to this expression for a long time. Anyway, my question is - is the derivative of e^x exact? That is with absolute precision, the derivative of e^x is EXACTLY e^x? Sorry if this seems like a silly question, I would really like to know if my math instructor is right on...

What if the proof for differentiating and integrating e^x. For d/dx (e^x) i used the chin rule and did u = x y = e^u dy/du = ue^u-1 du/dx = 1 dy/du*du/dx = ue^u-1 so you get xe^x-1 but that's not right. I don't even know where to start with intergration. Can anyone show me...

Homework Statement I am looking for a way to solve the equation e^x + x = c, with c being some constant. I know that I could get an answer from graphing, but I would like to know how to solve an equation like this algebraically. How is this possible? Homework Equations None. The...

Homework Statement Can you help me simplify the following equation: -e^((-1/2)*x^2)*(x^2-1)+2*e^((-1/2)*x^2)*x. Homework Equations The Attempt at a Solution I've been guessing that you can combine the e^((-1/2)*x^2) components and thus end up with (x^2-1)x+e^((-1/2)*x^2)*x...

I have an equation I need to solve by using undetermined coefficients: y'' - y' = ex The auxiliary equation is: r2- r = 0 , so 2 real roots (R1=0, R2 = 1) So, yc(x) = C1 + C2ex Now for the particular solution: I can try Aex but this is already present in the complementary...

Homework Statement If g(x) = 3 + x + e^x, find g^{-1}(4) Homework Equations Not sure. The log laws don't seem to apply. Probably laws/rules related to the number e. The Attempt at a Solution So I know the whole process and technically have this solved, but not because I understand...

Homework Statement Show that y(t) = e^t is a solution of y'' - y = 0, Homework Equations integral of e^x dx = e^x +c derivative of e^x = e^x The Attempt at a Solution set m = d(e^t)/dt, which also = e^t then dm = e^t then d(m)/dt = e^t if y(t) = e^t is a solution integrate...

Homework Statement I have done an integration and ended up with the result [-c/2 * [e^(-2x)]] |^infinity_0 = 1 The solution is that c=2 so that means to me that e^(2x) must turn into minus 1 for it to equal 1... but I'm not sure.. I've got graphcalc so I've been staring at the graph and...