Thread: Taylor series and error approximations

1. Taylor series and error approximations

Hello,

Im having some trouble with the error approximations in relation to Taylor series.

For example $$f(x) = x^{1/3}$$ about $x=8$; approximate $9^{1/3}$

$$f(x)= (x+8)^{1/3}$$
$f'(x) = 1/3(x+8)^{-2/3}$
$f''(x) = -2/9(x+8)^{-5/3}$

$f(1) = 2 + 1/12 - 1/288$

However i just can't get my head around how to do the error approximation.

/Jones

2. note that the series is alternating ... error < |first omitted term|

3. Hmm, how do you mean?