**Problem : **
Approximate *e*^{0.1} to within 10^{-3} using Taylor's formula.

r_{n}(x) = x^{n} = x^{n} < x^{n} |

where

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 - + - + ^{ ... } |

The absolute value of the error term in Taylor's formula is

| r_{n}(x)| = x^{n} = | x|^{n}≤ |

Noting that |

sin(- 0.1) (- 0.1) - –0.09983 |

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