1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Expanding A Taylor series.

  1. May 20, 2009 #1


    User Avatar

    1. Hi, I am new to taylor series expansions and just wondered if somebody could demonstrate how to do the following.

    Find the Taylor series of the following functions by using the standard Taylor series also find the Radius of convergence in each case.

    1.log(x) about x=2

    2.[tex](3+2x)^{\frac{1}{3}}[/tex] about x=0.

    3. When it says standard power series what does it mean? As I don't know what it means I have been unable to get started.
  2. jcsd
  3. May 20, 2009 #2


    User Avatar
    Homework Helper

    There ought to be a definition of the Taylor expansion in the text you're using or your class notes. Taylor expanding a function about a point x=a is done by:

    f(a)+\frac {f'(a)}{1!} (x-a)+ \frac{f''(a)}{2!} (x-a)^2+\frac{f^{(3)}(a)}{3!}(x-a)^3+ \cdots

    A standard power series looks like this [itex]f(x)=\sum_{n=0}^\infty a_n (x-a)^n[/itex].
    Last edited: May 20, 2009
  4. May 20, 2009 #3


    User Avatar

    Ok, I think I see how to do the expansion for log(x) now Is this right? Is there a way to include the first log(2) in the summand?

    [tex]\log(2) + \sum_{n=1}^{\infty} \frac{(-1)^{n+1}(x-2)^n}{n2^n}[/tex]

    and I then applied the ratio test to get that the thing converges for 0<x<4 (that can't be right can it?) Using the cauchy root

    test I get R=2.
    Last edited: May 20, 2009
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Expanding A Taylor series.
  1. Expanding a series (Replies: 11)

  2. Taylor Series (Replies: 1)

  3. Taylor Series (Replies: 2)

  4. Taylor series (Replies: 15)