## If and only if in analysis |

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### Contents

INTRODUCTION SETS AND FUNCTIONS | 1 |

LIMITS AND CONTINUITY | 17 |

DIFFERENTIATION | 48 |

Copyright | |

4 other sections not shown

### Common terms and phrases

absolutely convergent analytic bounded functions bounded sequence calculus Cauchy product chapter closed interval a,b cluster point composite function consider the function consider the sequence convergent series defined on 0,l definition Dirichlet's test discontinuous domain entiable entire real line exist f and g f dx f is continuous f is Riemann finite number function defined function f harmonic series Hence indeterminate forms infinite series integrable on a,b interval 0,l l'Hopital's rule least upper bound Let f lim f lim f(x lim+ limit point maximum mean value theorem monotonic n+l n1 open interval open set origin partial sums positive power series quence quotient radius of convergence rational numbers reader real numbers Riemann integrable second derivative sequence f sequence of functions sequence of partial series converges series of functions sin(l/x subset sufficient condition suppose Taylor series Theorem l0 tinuous tion uniform convergence uniformly bounded vergent zero