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Maclaurin polynomials problem

  1. Jan 10, 2007 #1
    1. The problem statement, all variables and given/known data

    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)


    2. Relevant equations

    pn(x)= f(0) + f'(0)x + [f''(0)/2!](x)^2 +[f'''(0)/3!](x)^3 + .... + [f^(n)(0)/n!](x)^n


    3. The attempt at a solution

    I know that I need to find up to the 4th derivative using f(x)=ln(x) and then simply use the maclaurin polynomial equation up to a certain point for n = 0, 1, 2, 3, 4 .. n.

    The only problem is I can't remember how to FIND derivatives of ln(x)!
    I don't really understand how to find the nth polynomial in sigma notation either..

    Thank you!
     
  2. jcsd
  3. Jan 10, 2007 #2
    What integrates to give ln(x)? (How is it defined?)
    The nth polynomial bit will probably become clearer once you've written down a few of the derivatives.
     
  4. Jan 10, 2007 #3
    Well, I thought (1/x) integrates to ln(x), but I wasn't sure about the derivative...
     
  5. Jan 10, 2007 #4
    So what's the realtionship between integrating and differentiating?
     
  6. Jan 10, 2007 #5
    OH okay i just realized at the beginning of the problem i was referring to ln(x+1) and then somehow i changed it to ln(x). i understand about the relationship between ln(x) and 1/x, i just need help with the derivative of ln(x+1)

    thank you!
     
  7. Jan 10, 2007 #6
    Try letting u=x+1
     
  8. Jan 10, 2007 #7
    soo.. ln(u)du =1/(u) ? so its just 1/(x+1) ?

    wow, i thought it was alot harder for some reason.
     
  9. Jan 10, 2007 #8
    That's right.
     
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