Maclaurin series Definition and 155 Threads

Homework Statement Compute the 9th derivative of f(x) = \frac{\cos\left(3 x^{4} \right) - 1}{x^{7}} at x=(0) Homework Equations f(x)=\sum^{\infty}_{n=0} \frac{f^{(n)}(c)}{n!}x^n cos(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n)!}x^{2n} The Attempt at a Solution The correct answer is...

Homework Statement Write the Machlaurin series for : f(x) = (2x)/(1+x2) Homework Equations The Attempt at a Solution I tried finding all the derivatives (aka f(x), f'(x), f''(x), etc..) but the equations started getting longer and longer and would always result in 0 when x=0...

Homework Statement Find the first four terms of the Maclaurin series for f(x) = (x+1)^-2

Since ln(0) doesn't exist, this question is futile right? I am tasked with finding a Maclaurin powerseries for ln(x) and to find out how many times I have to run that series to get a accurate answer for ln(1.5). What should I do? Should I find the taylor series for ln(1.5) for should I...

Homework Statement f(x) = e^(x^2) * sin(x) Find the value of the 3rd derivative at x = 0. Homework Equations e^x = 1 + x + x^2/2! + ... + x^n/n! sin(x) = 1 + x^3/3! - x^5/5! + ... + x^(2n+1)/(2n+1)! * (-1)^(n-1) The Attempt at a Solution I know I should plug in the two...

Homework Statement How can I calculate it for \frac{1}{1+cos^2(x)} by using the fact that \frac{1}{1+x^2} = 1 - x^2 + x^4 - ...? Homework Equations Given in the problem. The Attempt at a Solution I tried letting u = cos(x), then \frac{1}{1+cos^2(x)} = \frac{1}{1+u^2} = 1...

Homework Statement I got a few functions I need to expand to series using Maclaurin forumlas. Homework Equations http://mathworld.wolfram.com/MaclaurinSeries.html The Attempt at a Solution So here are the ones I managed to do: f= \sqrt{1-x^2-y^2} writing it in another form...

Homework Statement Wikipedia states that the Maclaurin Series expansion of the Lorentz factor is http://en.wikipedia.org/wiki/Lorentz_factor" Homework Equations Relevant equations are all found in that article The Attempt at a Solution I don't see how this comes about. My attempt...

Homework Statement find coefficient of x^4 in the MAclaurin series for f(x)=e^sinx Homework Equations ok... so taking derivatives 4 times for this function...gave me a mess! @.@ can someone help me in simplying the derivatives...? 1. cosxe^sinx then for 2. is it...

Homework Statement The Maclaurin series for a function f is given by \sum\frac{x^n}{2n}. What is the value of f(4)(0), the fourth derivative of at x = 0? a.) 1 b.) 2 c.) 3 d.) 4 e.) 5 Homework Equations The Maclaurin Series is the infinite series centered at x = 0 with the following...

Homework Statement Find the first six nonvanishing terms in the Maclaurin series solution of the initial value problem (x^2 - 3)y''(x) + 2xy'(x) = 0 where y(0) = y0 and y'(0) = y1. Homework Equations The Attempt at a Solution Should with just something like Φ(x) such that Φ(x) =...

Homework Statement Find the Maclaurin Series for g(x)= (4)/(4+2x+x^2) and its interval of convergence. Homework Equations I know the Maclaurin Series usually involves taking derivatives but every other problem I've done so far has had a degree that I've solved to. So, other than the general...

Homework Statement Find the Maclaurin series for f(x)= 1/ (1+x+X2) Homework Equations The Attempt at a Solution I think the book says I can just divide 1 by the Maclaurin series of (1+x+X2). And when i do this the original function is the answer (which makes sense). But when...

Homework Statement (1 pt) Compute the 9th derivative of: f(x) = \frac{cos(6x^4)-1}{x^7} at x=0. Homework Equations Hint: Use the MacLaurin series for f(x). The Attempt at a Solution I have tried many weird ways and cannot come up with the correct numerical answer. I've...

Find the first few terms of the Taylor Series around x=0...? of the function f(x)= {x/(e^x - 1) , x =/ 0} {1 , x=0} the function is piecewise. up to and including the term involving x^2 It says to not compute derivatives of f but to use the formula for the...

Homework Statement 5) For each of the series below, write the series in summation notation and give the first five terms of the series. Also give the radius of convergence of the series. a) Use the series for \frac{1}{1 - x} to find the Maclaurin series of f(x) = \frac{1}{(1-2x)^3}...

Hey, here's is my problem as the exam states it: A) Write out the first four non-zero terms of the Maclaurin Series for F(x) = (1+X^{7})^{-4} Give all of the coefficients in exact form, simplified as much as possible. B) Find the exact value of the 21st order derivative of F(x) =...

Hi all, I am trying to work out a series expansion for ln ((x+1)/(x-1)). I have got the series expansion for ln(x+1) ie x- (x^2/2) + (x^3/3) - (x^4/4) ... and for ln(x-1) -x- (x^2/2) - (x^3/3) - (x^4/4) ... Can I tie these two together to get the series for ln...

I have the following problem: find the first 3 non-zero terms in the Maclaurin series for the function: e-x2 + Cos[x] I know in this case, the series behave like polynomials and I have done the following. The left expression is the first 3 terms of the e portion of the problem, and the...

Okay I was given this problem as a challenge question. It simply says expressing 2x power as a Maclaurin Series. At first, following an example given by my instructor, I thought that by examining the function as I took multiple derivatives I could find a pattern. By as you can imagine taking...

Homework Statement Hey. I need to develop this function into maclaurin series. Did I do it correctly? Homework Equations The Attempt at a Solution

Homework Statement find the maclaurin series of e^(3x) + e(-3x) Homework Equations The Attempt at a Solution I'm not sure about finding taylor and maclaurin series, I understand perfectly how to find the terms of the series...But how do I put it into a general term do I just...

Homework Statement find the Maclaurin Series: f(x)=(e^x - cos(x))/x Homework Equations The Attempt at a Solution I'm not really sure what to do I do know the Maclaurin series of cos(x) I was thinking that using this known series then doing e^x - the known series then...

Homework Statement Show that the function defined by (stepwise) f(x)= e^(-1/x^2) if x =/ 0 = 0 if x=0 is NOT equal to its Maclauren series. Then graph the function and comment on its behavior near the origin.The Attempt at a Solution Well, I honestly don't know how to...

Today, we're taught that MacLaurin series is just another name for Taylor series at x = 0. Then what is the speciality of it? Why doesn't x = 1 or x = 2 have a special name?

Find the Maclaurin series for f(x) = (x^2)(e^x) the book suggests obtaining the Maclaurin series of f(x) by multiplying the known Maclaurin series for e^x by x^2: (x^2)(e^x) = (x^2)(1 + x + (x^2)/2! + (x^3)/3! + (x^4)/4! + ...) = x^2 + x^3 + (x^4)/2! + (x^5)/3! + (x^6)/4! + ... =...

Hey all. We never covered the Maclaurin series (covered Taylor) but these questions are on my review for my final. Homework Statement Compute the 9th derivative of: arctan((x^3)/2) at x=0 f^9(0)=? Homework Equations Use the MacLaurin series for f(x) The Attempt at a Solution...

Find the MacLaurin polynomial of degree 4 for f(x) f(x)= (integral from 0 to x) sin(3t^2) [f^(n)(0)/n!]*x^n The Attempt at a Solution - I took the 4th derivative of sin(3t^2) and got: f''''(x)= -108sin(3t^2)-1296t^2cos(3t^2)+1296t^4sin(3t^2) Not real sure what to do from...

For the function f(x) = (10x^2) e^(-2x), I calculated the first term of the Maclaurin series to be 0. However, for the second term, I also calculated it to be 0, but apparently this is wrong. Shouldn't the second term be f'(x) = 10x^2 * -2e^(-2x) + e^(-2x) * 20x? Or what am I doing...

Im really having trouble wrapping my mind around the topic of maclaurin series, my problem requires me to find the maclaurin series of f(x) = 1/(1+x^2), then use that to find the maclaurin series of g(x)= arctan(x)...i don't even know where to begin.

I was asked to find dy/dx of inverse tan of x , which is 1/(1+x^2) Then its says, using that dy/dx ^^^^^ equal to a particular series, find the first 4 terms of inverse tan of x. I'm confused? What is it asking here??

Homework Statement find a_{n} for f(x)\ =\ \frac{1}{1+3x} The Attempt at a Solution I got: f(0) = 1 f'(0) = -3 f''(0) = 9 The answer I ended up with was: a_{n} \ = \ {(-1)}^n\frac{3^n}{n!} However, the answer in the back of my book has the same answer except it's not divided by n!.

Please Refer to the attachment, I'm new to the forums and am not sure how to type Math Terms. I've been working on this for a couple of days now and i can't get anywhere near an answer. Any Help is MUCH appreciated! Thanks!

I have been asked to differentiate cos x and six...the maclaurin series versions... I have done the general and specific terms as shown below. Im not sure if these are correct? thanks General Terms cos x = ∑ (-1)n (x^(2n) / (2n)!) COS x = ∑ (-1)n (x^(2n+1)/ (2n +1) / (2n)!)...

For my homework in my class, I'm supposed to find the first 3 non-zero terms of the Maclaurin series of f(x) = Integral sin(t)/t dt evaluated from 0 to x. I'm fairly sure that sint/t dt has no integral, so I'm lost in my search for the solution. Can you guys point me in the right direction?

MATLAB HELP! -- Maclaurin series Hi, i have absolutely no programming experience with MATLAB and really need it. We have been assigned 2 problems using MATLAB and a bunch of others that don't need matlab. I was wondering if someone could show me what to do for the two needed to be done in...

Represent the function 5ln(7-x) as a power series, i.e., Maclaurin series, C_0= C_1= C_2= C_3= C_4= i got C_0 = 5 ln (7-0) and i think C_1 = 5/(7-1) but its wrong the textbook says that C_1 will be the derivative of C_0 anyway... please give me some hint

Hi, hopefully you guys can point me in the right direction. The problem says to determine the number of terms necessary to approximate cos(x) to 8 significant digits using Maclaurin series approximation for x = .3*pi. I don't really have a problem with the actually question, my problem comes...

I have the Maclaurin series for cos (x), is their a way to find its radius of convergence from that? ALSO Is there a trick to find the shorter version of the power series for the Maclaurin series, I can never seem to find it so instead of the long series with each term but like E summation (the...

I have to find the first three non-zero terms in the Maclaurin series for the function sec(x). I guess I have to use the known Maclaurin series for cos(x) and doing 1/cos(x) series with long division. I tried that but didn't get anywere close to the right answer. Could anyone please help me?

So I'm studying Taylor Series (I work ahead of my calc class so that when we cover topics I already know them and they are easier to study..) and tonight I found a formula for taylor series and maclaurin series, and i used them to prove eulers identity. However, I don't really know much about...

PLEASE HELP need conformation on derivative of e^(x-1) Can't remember if derivative of e^(x-1) is e^(x-1) or if it changes. PLEASE HELP!

obtain the maclaurin series expansions of the following: ln(1+e^x) ok I am quite lost..i assume you set it equal to f(x) then differentiate..but what happens when you differentiate that? also question (b) is \frac{x}{(e^x-1)} does that work down to (e^x - 1)^-x ? and if so..would you then...

I've looked at a number of explanations for the Maclaurin series of cos(x) yet none have given an easily understood answer, i was wondering if anyone has a way of explaining it when it is used as only a part of a function eg. use that Maclaurin series of cos(x) to obtain the Macalurin series...

Can you please offer any hints or suggestions on how to do these two problems: 1) Find the Maclaurin series of (x^2 + 1)/(3x^2 + 2x - 1). Should I perform long-division first? I can't seem to find any repeating pattern... 2) Evaluate the integral sqrt(12-4x-x^2) from x=2 to x=6. I...

My question is as follows: Let f (x) = (1+x)^(1/2) – (1-x)^(1/2). Find the Maclaurin series for f(x) and use it to find f ^5 (0) and f ^20 (0). I got: X + Riemann Sum { [ (-1)^(n-1) 1x3x5**x(2n-3) ] / (2^n) x n！} X^n (after combining two Riemann Sums together). And I got (7！5！) / 16 5！ =...

I need some peer review of this quesion. Let f(x)=x^2e^{-2x^2} (a) find the maclaurin series of f (b) find the 100th degree maclaurin polynomial of f. for part a i have:\sum_{n=0}^{\infty}\frac{(-2)^nx^{2n+2}}{n!} and for b:\sum_{n=0}^{99}\frac{(-2)^nx^{2n+2}}{n!}

I'm supposed to find the following function as a Maclaurin Series. Please check if I'm correct. f(x) = ln(1+x) \sum \frac{\(x^n)((-1)^{n+1})}{n} and that sum goes from n=1 to \infty I also have to find the following functions as power series so please check it for me! f(x) =...

i have trouble expandind f(x)= (sin2x)^2 into Maclaurin series for sin(x) Maclaurin series is \sum^{\infty}_{n=0} (-1)^n \frac{x^{2n+1}}{(2n+1)!} probably the key is to change (sin2x)^2 into new shape. I found that (sin2x)^2=2sin(2x^2), but that coefficent 2 is bothering me, what to do?

We learned that the Maclaurin series for sin(x) was \sum^{\infty}_{n=0} (-1)^n \frac{x^{2n+1}}{(2n+1)!} Is the Maclaurin series for sin(2x) the same, except with x replaced by 2x?