1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Staff Emeritus
    Science Advisor

    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Taylor polynomial help
Loading...