Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

xartaan

Taylor Series question here: So I am learning about Taylor series/polynomials and I am deriving some of the common functions just to get comfortable with the process. My problem is with ln(x). My process for finding taylor polynomials has been to take a few derivatives so in this case \[f(x)=\ln(x)....f'(x)=\frac{ 1 }{ x }...f''(x)=\frac{ -1 }{ x^2 }....f'''(x)=\frac{ 2 }{ x^3 } \] etc... But for the next step I have been evaluating each term at x=0 to find the general term. How can I do this for ln(x) since as far as I know, ln(0) isn't valid? (at least at my level of maths)

  • one year ago
  • one year ago

  • This Question is Closed
  1. satellite73
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\ln(x)\] therefore has no taylor series expansion at \(x=0\)

    • one year ago
  2. TuringTest
    Best Response
    You've already chosen the best response.
    Medals 2

    You don't take the taylor series of lnx about x=0 for the reason you discovered. It's much more common to take it around x=-1, or expand ln(x+1)

    • one year ago
  3. satellite73
    Best Response
    You've already chosen the best response.
    Medals 1

    as you can see every term will be undefined you can expand at 1 say

    • one year ago
  4. satellite73
    Best Response
    You've already chosen the best response.
    Medals 1

    what @TuringTest said

    • one year ago
  5. xartaan
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok I will try from a different x then. I guess my confusion was just about finding a general term. I will expand at a different point and see if I can get it.

    • one year ago
  6. xartaan
    Best Response
    You've already chosen the best response.
    Medals 0

    Aha! That worked perfectly! Substituting x=1. Thanks guys!

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.