Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Calc 3 question

  1. Mar 23, 2010 #1

    sportlover36

    User Avatar

    how can i find a power series representation for a function like f(x)= ln(1+7x)?
     
    sportlover36, Mar 23, 2010
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. Mar 23, 2010 #2

    Mark44

    User Avatar
    Insights Author

    Staff: Mentor

    There are at least two ways. One is very mechanical and involves taking the derivatives of your fucntion. The other is probably a lot quicker. Can you find a power series for 7/(1 + 7x) = 1/(x + 1/7)? What's the connection between ln(1 + 7x) and 1/(x + 1/7)?
     
    Mark44, Mar 23, 2010
  4. Mar 23, 2010 #3

    sportlover36

    User Avatar

    Im not really sure what the connection is but i got this at the answer...the sumation from n=1 to infinity -7x^n/n
     
    sportlover36, Mar 23, 2010
  5. Mar 23, 2010 #4

    Mark44

    User Avatar
    Insights Author

    Staff: Mentor

    The connection is that d/dx(ln(1 + 7x) = 7/(1 + 7x), or conversely, that ln(1 + 7x) = [itex]\int[/itex]7/(1 + 7x) dx.

    If you didn't understand that connection, how did you get the result that you got? BTW, I'm not sure that your result is right.
     
    Mark44, Mar 23, 2010
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook