## Polynomials, power series, and calculus |

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### Contents

BACKGROUND MATERIAL | ix |

POLYNOMIALS | 15 |

FUNCTIONS HAVING POLYNOMIAL | 33 |

Copyright | |

7 other sections not shown

### Common terms and phrases

algebraic antiderivative ao+ai approximation to f arc length arithmetic sequence binomial theorem calculus Cauchy sequence circle class P(t coefficients continuous functions coordinate Corollary 4-7 cos-i cos2 curvature curve definition denoted differences divergent dominates g elementary Examples Exercises expression fact function defined function f function whose value given graph half plane infer infinite sequence infinite series instance interval of convergence interval x—t inverse least upper bound Lemma Let P(x lower bound MacLaurin series mathematics minimum modulo x—t)n+i monomial notation oriented angle osculating circle partial sum sequence polynomial functions polynomial of degree polynomial P(x positive integer positive number positive real numbers power series Proof Prove r-th root radius radius of convergence rate of change rational number reciprocal relative maximum residue of A(B(x Riemann integral sequence of order series converges set of numbers Show sum function Taylor series Taylor's Theorem term sequence unknown function zero