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Homework Help: More Taylors expansion

  1. May 19, 2008 #1
    I still need help with my first Taylors expansion thread, but this is a seperate problem

    1. The problem statement, all variables and given/known data

    a) Give the formula for the Taylor expansion of the function f(x) about the point x=a. You should include the formula for the coeffiecients of the expansion in terms of the derivatives of f(x)
    b) Find the first three non-zero terms of the Taylor expansion about x=1 of the function
    f(x)=exp(x^3-1)

    2. The attempt at a solution

    a)
    f(x + a) = f(a) + xf'(a) + x^2f''(a)/2! + ... + x^nf^n(a)/n! ... where f^n(a) means the nth derivative of f(a)

    I think I might have missed the point of this question.

    b)
    f(x+1) = 1 + 3x^3.e^(3x-1) + [9x^6.e^(3x-1)+6x^3.e^(3x-1)]/2

    I'm assuming here that exp(x^3-1) means e^(x^3-1), but this isn't notation that's used anywhere else on the paper.
     
  2. jcsd
  3. May 19, 2008 #2
    Taylor expansion about x = a by definition:

    f(x) = f(a) + (x-a)*f'(a) + (x-a)^2/2!*f''(a) + ...
     
  4. May 19, 2008 #3

    Defennder

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    Homework Helper

    Use the formula:

    NumberedEquation1.gif
     

    Attached Files:

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