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Taylor's Series problem help

  1. Nov 29, 2009 #1
    1. The problem statement, all variables and given/known data
    Expand f(x)=x^3 + 3x^2 +15x -10 in powers of x-1


    2. Relevant equations

    Taylor's Series, Maclaurin's series

    3. The attempt at a solution

    I dont know how to start...I do have an idea of both the theorems but dont know how to apply it to this situation.

    plz help...sem exams in a week's time!!!
     
  2. jcsd
  3. Nov 29, 2009 #2

    zcd

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    Re: Series

    x-1 means centered about x=1; the polynomial has only 4 relevant derivatives so just use the formula
     
  4. Nov 29, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: Series

    One way to do this, without using Taylor's series, is to let u= x-1 so that x= u+1. Your polynomial becomes [itex](u+1)^3 + 3(u+1)^2 +15(u+1) -10[/itex]. Expand that in powers of u and, finally, replace u by (x-1) to get the polynomial in powers of x-1.

    But simpler is to use the Taylor's series formula:
    f(a)+ f`(a)(x-a)+ f``(a)/2(x-a)^2+ f```(a)/3! (x-a)^3+ ...
     
  5. Nov 29, 2009 #4
    Re: Series

    thanks
     
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