## Calculus with analytic geometryThe aim of this major revision is to create a contemporary text which incorporates the best features of calculus reform yet preserves the main structure of an established and well-tested calculus course. The multivariate calculus material is completely rewritten to include the concept of a vector field and focuses on major physics and engineering applications of vector analysis. Covers such new topics as Jacobians, Kepler's laws, conics in polar coordinates and parametric representation of surfaces. Contains expanded use of calculator computations and numerous exercises. |

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### Contents

CHAPTER 6 APPLICATIONS OF THE DEFINITE | 307 |

CHAPTER 7 LOGARITHMIC AND EXPONENTIAL | 349 |

INVERSE TRIGONOMETRIC AND HYPERBOLIC | 413 |

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### Common terms and phrases

algebra angle antiderivative approximation asymptotes axis calculator called circle complex numbers computer algebra system concave constant continuous function cosh curve decreasing defined definite integral denote derivative differential equation distance diverges domain dy/dx ellipse endpoint Evaluate Example Exercise Set Express Find the area Find the volume formula geometric given Hint horizontal hyperbola improper integral indeterminate form inequality inverse L'Hopital's rule lim fix limit logarithms Maclaurin series mathematics maximum midpoint minimum value negative notation obtain open interval parabola parametric equations partial sum particle polar coordinates polynomial positive problem proof Prove radians radius real numbers rectangle region enclosed result satisfies secant line sequence series converges Show shown in Figure side Simpson's rule sin2 sinh Sketch the graph slope Solution solve Squeezing Theorem subintervals substitution tangent line variable velocity vertical x-axis y-axis y-intercept yields zero