Taylor Error 1

Taylor Error 1 - Taylor Error: Actual, Alternating Series...

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Taylor Error: Actual, Alternating Series and LaGrange By: Rachel Manser Actual Error This is the real amount of error, not the error bound (worst case scenario). It is the difference between the actual f(x) and the polynomial. Steps: 1. Plug x-value into f(x) to get a value. 2. Plug x-value into the polynomial and get another value. 3. The difference between the two is the error. Example: F(x) = 1 1 x - = 1+ x + 2 x + 3 x + 4 x + …… Approximate f(.1) using a 2 nd degree Taylor polynomial F(.1) = 1 1 .1 - = 1.111111… P 2 (.1) = 1 + (.1) + (.1) 2 = 1.11 Error = f(.1) - P 2 (.1) = 1.111111… – 1.11 = .001111…. Alternating Series If a series is alternating and decreasing, the error bound (worst case scenario) can be found by taking the absolute value of the n+1 term. F(x) = 1 - 1 2 + 1 3 - 1 4 + 1 5 - 1 6 + . ... + 1 ( 1) n n + - F(x) 1 - 1 2 + 1 3 - 1 4 + 1 5 Find the error bound of the above approximation of F(x). Error bound = 1 6 - = 1 6
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La Grange This method uses a special form of the Taylor formula to find the error bound of a polynomial approximation of a Taylor series. The La Grange Formula
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Taylor Error 1 - Taylor Error: Actual, Alternating Series...

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