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Taylor Polynomial

  1. Sep 28, 2005 #1

    I have found the following TP (n=4) for g(x) = (1+5x)^1/5
    P4(x) = 1+x-2x^2+6x^3-21x^4

    Then they ask me to show that 0<E4(x)<80x^5 when x>0.

    I don't know how to start, or exactly what Im supposed to show...?

    I have found E4(x) to be( 399/[5(1+5X)^24/5] ) *x^5...

    And 0<X<x ...?
  2. jcsd
  3. Sep 28, 2005 #2


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    Science Advisor

    To show that the error is LESS than something, you want to think about the X that gives the LARGEST possible error. Since X is in the denominator, the largest value of the fraction will be when X= 0. If you take X= 0 what is that value in the parentheses? (Gosh, 399 is awful close to 400!)
  4. Sep 28, 2005 #3
    Oh now I see how I get 0<E4(x)<80x^5

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