Maclaurin Definition and 199 Threads

Maclaurin or MacLaurin is a surname. Notable people with the surname include:

Colin Maclaurin (1698–1746), Scottish mathematician
Normand MacLaurin (1835–1914), Australian politician and university administrator
Henry Normand MacLaurin (1878–1915), Australian general
Ian MacLaurin, Baron MacLaurin of Knebworth
Richard Cockburn Maclaurin (1870–1920), US physicist and educator

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  1. M

    Finding the Laurent Series for 1/(x+3) around x=2

    Homework Statement I know the sum of the Laurent series (around x=2) is equal to \frac{1}{x+3} But I can't find what the series is from this information alone. Homework Equations In the textbook, you have (for -1 < x < 1): \frac{1}{1-x} = \sum_{n=0}^{\infty}x^n and for |x|>1 I know...
  2. B

    Can I Combine the Series for ln(x+1) and ln(x-1) to Expand ln((x+1)/(x-1))?

    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...
  3. J

    Multiplication of Maclaurin Series

    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...
  4. D

    Maclaurin Series, expressing 2^x as a M series.

    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...
  5. A

    Develop this function into maclaurin series

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

    Maclaurin Series: Find e^(3x) + e(-3x)

    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...
  7. P

    Find Maclaurin Series for f(x) = (e^x - cos(x))/x

    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...
  8. F

    Proving Non-Equivalence of e^(-1/x^2) and Maclaurin Series Graph Near Origin

    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...
  9. S

    MacLaurin Series: Exploring Speciality & Uniqueness

    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?
  10. G

    Find the Maclaurin series for f(x) = (x^2)(e^x)

    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! + ... =...
  11. H

    Find function is analytic on R and has Maclaurin expansion

    Prove the function is analytic on R and find its Maclaurin expansion. (a) e^{x}cosx Well, I did some work. I can show that e^{x}=\sumx^{k}/k! cosx=\sum((-1)^{k}x^{2k})/(2k)! are analytic and have the above Maclaurin expression. My problem is multiplying these two...
  12. M

    Maclaurin Series homework help

    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...
  13. S

    Finding Maclaurin Series of f(x)=sin(3t^2) up to Degree 4

    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...
  14. C

    Calculating Maclaurin Series for f(x) = (10x^2) e^(-2x)

    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...
  15. B

    Why Is a Taylor Series More Accurate Near Its Expansion Point?

    Hi I have some questions. If you're doing a MacLaurin expansion on a function say sinx or whatever, if you take an infinite number of terms in your series will it be 100% accurate? So will the MacLaurin series then be perfectly equal to the thing you're expanding? Also I don't really...
  16. K

    What is the process for finding Maclaurin series?

    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.
  17. J

    MacLaurin series, inverse tan of x

    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??
  18. K

    Maclaurin Series: Find a_n for f(x) = 1/(1+3x)

    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!.
  19. C

    Maclaurin series of the function

    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!
  20. J

    Comparing Maclaurin Series of cos x and sin x

    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)!)...
  21. R

    Remainder Estimation Theorem & Maclaurin Polynomials :[

    Homework Statement Use the Remainder Estimation Theorem to find an interval containing x=0 over which f(x) can be approximated by p(x) to three decimal-place accuracy throughout the interval. Check your answer by graphing |f(x) - p(x)| over the interval you obtained. f(x)= sinx p(x)=...
  22. R

    How to Find Maclaurin Polynomials for ln(x) in Sigma Notation?

    Homework Statement Find the Maclaurin polynomials of orders n=0, 1, 2, 3, and 4, and then find the nth Maclaurin polynomials for the function in sigma notation: f(x)= ln(1+x) Homework Equations pn(x)= f(0) + f'(0)x + [f''(0)/2!](x)^2 +[f'''(0)/3!](x)^3 + ... + [f^(n)(0)/n!](x)^n...
  23. F

    Maclaurin Power Series for 1/(4x^2+1) and Integration of e^-x^2

    I was hoping someone could check my work: Find the maclaurin power series for the function: a. f(x)=1/(4x^2+1) b. f(x)= \int e^-x^2 dx For a I got (-1)^n*2nx^n. For b I don't know where to start.
  24. F

    Maclaurin Series for an Integral

    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?
  25. F

    MATLAB MATLAB HELP - Maclaurin series

    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...
  26. K

    Finding Maclaurin Error < 0.0001 for f(x)=cos(2x) at x=0.6

    Here's the problem: Determine the degree of Maclaurin polynomial required for the error to be less than .0001 if f(x)=cos(2x) and you are approximating f(0.6) I really don't know what I am doing. Here's what I've tried to do: Rn(.6) = ( (f^(n+1)(z)) / (n+1)! ) (.6)^(n+1) I don't...
  27. B

    Maclaurin Series Expansion of 5ln(7-x)

    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
  28. O

    4th order Maclaurin Polynomial - Help with error approximation

    I have the the follow 3rd order polynomial approximation for e^3x f(x) = e^{3x} \approx 1 + 3x + \frac{9}{2}x^2 + \frac{9}{2}x^3 In an earlier part of the problem, I found f\left( {\frac{1}{3}} \right) = e^{3\left( {\frac{1}{3}} \right)} \approx 1 + 3\left( {\frac{1}{3}} \right) +...
  29. N

    Analysis of $e^{ix}$ by Maclaurin Formula

    Analyze by Maclaurin formula: $e^{ix}$
  30. I

    MATLAB How to Use Loops in MATLAB for Maclaurin Series Approximation?

    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...
  31. B

    Maclaurin Series used to find associated radius of convergence Q

    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...
  32. S

    Find First 3 Terms of MacLaurin Series for sec(x)

    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?
  33. kreil

    Studying Taylor and Maclaurin Series

    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...
  34. K

    Is the Derivative of e^(x-1) Simply e^(x-1)?

    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!
  35. B

    Maclaurin Series for ln(1+e^x) and \frac{x}{(e^x-1)}

    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...
  36. L

    Question about the maclaurin serie and laplace transform

    Question about the maclaurin serie and the laplace transform. For maclaurin serie i wonder, the function used for teh maclaurin development must be derivativable to infinity? What is the difference between the fouri transform and the laplace transform? As i understood it, it's just the...
  37. M

    Understanding the Maclaurin Series of cos(x) for Use in Functions

    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...
  38. M

    Improper integral + Maclaurin series problem

    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...
  39. D

    Discover the Maclaurin Series for f(x) with Derivative Calculations

    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！ =...
  40. RadiationX

    How Accurate Is the Maclaurin Series for \( f(x) = x^2e^{-2x^2} \)?

    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!}
  41. R

    Verifying Maclaurin Series for f(x)=ln(1+x)

    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) =...
  42. V

    Maclaurin Series for Expanding sin(2x)^2: Step-by-Step Guide

    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?
  43. tandoorichicken

    Is the Maclaurin series for sin(2x) the same as the one for sin(x)?

    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?
  44. Y

    Need help with maclaurin series question

    its using the Maclaurin series, i have already worked out the equations: cos x = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + (x^8)/8! - (x^10)/10! + ... e^x = 1 + x + (x^2)/2! +(x^3)/3! + (x^4)/4! + (x^5)/5! + (x^6)/6! + ... how do i use these two results to obtain the first 6 terms on the...
  45. W

    Can someone help me understand Taylor and MacLaurin series?

    I am having difficulty understanding Taylor and MacLaurin series. I need someone to go through step by step and explain a problem from beginning to end. You could use the function f(x) = cos x. Also, could someone find the MacLaurin series of 1/(x^2 + 4) ? I just don't understand the basics of...
  46. P

    Find 1st 4 Non-Zero Terms Maclaurin Series

    Im helping my sis study for her exam but i can't remember how to find the first four non-zero terms of the maclaurin series
  47. D

    CLUELESS about a Maclaurin series

    CLUELESS about a Maclaurin series! I'm supposed to obtain a Maclaurin series for the function defined by f(x) = \left\{ \begin{array}{lc} e^{-1/x^2} & \mbox{ if } x \neq 0 \\ 0 & \mbox{ if } x = 0 \end{array} \right. I get immediately stuck as I find: f(0) = 0 f^{\prime}(0) =...
  48. A

    Can Anyone Prove the Maclaurin Series for ln(1+x)?

    Hello! Who can prove the maclaurin equations: ln(1+kv/mg)= kv/mg - k^2v^2/2m^2g^2 +... tellme at aminr@tebyan.net :smile:
  49. M

    Maclaurin Series and the general term

    using the sin and cos Maclaurin series, validate each of them using at least 3 values for x and determine how many terms are needed to provide reasonable accuracy. Find the General Term (Tn where n = 1, 2, 3, ...) for each expression and show that each correctly generates the terms of the...
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