## Calculus with Analytic GeometryFunctions and limits; The derivative; Applications of the derivative; The integral; Applications of the integral; Transcedental functions; Techniques of integration; Indeterminate forms and improper integrals; Numerical methods, approximations; Infinite series; Conics and polar coordinates; Geometry in the plane, vectors; Geometry in space, vectors; The derivative in n-space; The integral in n-space; Vector calculus; Differential equations. |

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### Contents

Preliminaries | 1 |

Functions and Limits | 36 |

The Derivative | 86 |

Copyright | |

16 other sections not shown

### Common terms and phrases

angle antiderivative approximate calculate centimeters Chain Rule circle concave constant continuous converges coordinates corresponding cos2 cosh critical points curve definite integral derivative distance diverges domain dy/dx ellipse endpoints Evaluate EXAMPLE 2 Find feet per second Figure 9 Find the area Find the equation Find the volume formula Fundamental Theorem given Hint horizontal hyperbola inequality interval inverse l'Hopital's Rule length lim f(x limit logarithms maximum Mean Value Theorem miles per hour minimum value notation obtain odd function parabola parametric equations plane polynomial positive number PROBLEM SET Proof Prove radians radius rational function rational number real numbers region bounded result revolving Riemann sum sec2 Section Show shown in Figure sin2 sinh Sketch the graph slope solid solid of revolution Solution Let solve square stationary point substitution Suppose tangent line triangle variable vector velocity vertical x-axis y-axis y-intercept zero