Problem : Approximate e ^{0.1} to within 10^{-3} using Taylor's formula.
The error term in Taylor's formula is
r _{n}(x) = x ^{n} = x ^{n} < x ^{n} |
e ^{0.1} 1 + 0.1 + = 1.105 |
Problem : Approximate sin(- 0.1) to within 10^{-5} . The Taylor series for sin(x) begins
x - + - + ^{ ... } |
| r _{n}(x)| = x ^{n} = | x|^{n}≤ |
sin(- 0.1) (- 0.1) - –0.09983 |