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!

Question about a tricky/difficult Taylor expansion of natural logarithm

  1. Mar 30, 2009 #1
    Can someone please tell me how to expand

    \ln(x + \sqrt{1+x^2})

    for small [itex]x[/itex]? I'd like to retain terms at least up to order [itex]x^5[/itex]. Thanks!
  2. jcsd
  3. Mar 31, 2009 #2
    Let f(x) = ln( x + sqrt(1 + x^2) ).

    Find f(0).
    Find f '(0)
    Find f ''(0)
    Find f '''(0)
    Find f ''''(0)
    Find f '''''(0)

    Then write f(x) = [f(0)x^0]/0! + [f '(0)x^1]/1! + [f ''(0)x^2]/2! + [f '''(0)x^3]/3! + [f ''''(0)x^4]/4! + [f '''''(0)x^5]/5!.

    Does that sound right?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook