the value of e.
SOLUTION: From Example 40 we know that f(x) = ex generates the Maclaurin
series
The Lagrange error bound is
To estimate e, we use x = 1. For 0 < c < 1, the maximum value of ec is e. Thus:
with error less than .Example 49 __
Find the Maclaurin series for ln (1 + x) and the associated Lagrange error bound.
SOLUTION:
Then
where the Lagrange error bound is
NOTE: For 0 < x < 1 the Maclaurin series is alternating, and the error bound
simplifies to , the first omitted term. The more difficult Lagrange
error bound applies for −1 < x < 0.