Example 51 __
Compute to four decimal places.
SOLUTION: We can use the Maclaurin series,
and let to get
Note that, since this series converges by the Alternating Series Test, R 5 is less
than the first term dropped:
so , correct to four decimal places.
Example 52 __
Estimate the error if the approximate formula
is used and |x| < 0.02.
SOLUTION: We obtain the first few terms of the Maclaurin series generated by
: Then
Note that for x < 0, the series is not alternating, so we must use the Lagrange
error bound. Here R 1 is , where −0.02 < c < 0.02. With |x| < 0.02, we see
that the upper bound uses c = −0.02: