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Homework Help: Taylor polynomial help

  1. Mar 12, 2007 #1
    1. The problem statement, all variables and given/known data

    I'm trying to make the nth degree taylor polynomial for f(x)=sqrtx centered at 4 and then approximate sqrt(4.1) using the 5th degree polynomial


    I know that the polynomials are found using the form:
    P(x)= f(x)+f'(x)x+f''(x)x^2/2factorial.....f^n(x)x^n/nfactorial

    so would P(4) just be:

    f(4)+f'(4)x + f''(4)x^2/2factorial + f'''(4)x^3/3factorial...

    and then would i just plug in 4.1 for x?

    thanks for your help...i would also appreciate any general comments on taylor polynomials as I don't really understand them. Thanks!
     
  2. jcsd
  3. Mar 12, 2007 #2

    Dick

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    You would plug in .1 for x. You are writing the Taylor expansion of f(4+x).
     
  4. Mar 12, 2007 #3
    but is what i wrote for P(x) the nth degree polynomial?
    Thanks
     
  5. Mar 12, 2007 #4

    Dick

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    What you wrote is a bit garbled. Here's a correction. Notice the different roles of x and a. a is the point you are expanding around and x is the displacement from a.

    P(a,x)= f(a)+f'(a)x+f''(a)x^2/2factorial.....f^n(a)x^n/nfactorial

    is the nth degree approximation to f(a+x).
     
    Last edited: Mar 12, 2007
  6. Mar 12, 2007 #5

    HallsofIvy

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    No. The taylor series "centered on 4" is f(4)+ f'(4)(x-4)+ f"(4)/2 (x-4)2+ ...+ f(n)(4)/n! (x- 4)^n
    Now let x= 4.1.

    Or use your polynomial with x= 0.1

     
  7. Mar 12, 2007 #6
    is there a general method to finding the nth degree polynomial? or is it always just f^n(a)x^n/nfactorial ?? Thanks!
     
  8. Mar 12, 2007 #7
    for any function in general...thanks!
     
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