PrefaceChapter 1 Linear Coordinate Systems. Absolute Value. Inequalities. Linear Coordinate System Finite Intervals Infinite Intervals Inequalities Solved Problems Supplementary ProblemsChapter 2 Rectangular Coordinate Systems Coordinate Axes Coordinates Quadrants The Distance Formula The Midpoint Formulas Proofs of Geometric Theorems Solved Problems Supplementary ProblemsChapter 3 Lines The Steepness of a Line The Sign of the Slope Slope and Steepness Equations of Lines A Point-Slope Equation Slope-Intercept Equation Parallel Lines Perpendicular Lines Solved Problems Supplementary ProblemsChapter 4 Circles Equations of Circles The Standard Equation of a Circle Solved Problems Supplementary ProblemsChapter 5 Equations and Their Graphs The Graph of an Equation Parabolas Ellipses Hyperbolas Conic Sections Solved Problems Supplementary ProblemsChapter 6 Functions Solved Problems Supplementary ProblemsChapter 7 Limits Limit of a Function Right and Left Limits Theorems on Limits Infinity Solved Problems Supplementary ProblemsChapter 8 Continuity Continuous Function Solved Problems Supplementary ProblemsChapter 9 The Derivative Delta Notation The Derivative Notation for Derivatives Differentiability Solved Problems Supplementary ProblemsChapter 10 Rules for Differentiating Functions Differentiation Composite Functions. The Chain Rule. Chain Rule Alternative Formulation of the Chain Rule Inverse Functions Higher Derivatives Solved Problems Supplementary ProblemsChapter 11 Implicit Differentiation Implicit Functions Derivatives of Higher Order Solved Problems Supplementary ProblemsChapter 12 Tangent and Normal Lines The Angles of Intersection Solved Problems Supplementary ProblemsChapter 13 Law of the Mean. Increasing and Decreasing Functions. Relative Maximum and Minimum Increasing and Decreasing Functions Solved Problems Supplementary ProblemsChapter 14 Maximum and Minimum Values Critical Numbers Second Derivative Test for Relative Extrema First Derivative Test Absolute Maximum and Minimum Tabular Method for Finding the Absolute Maximum and Minimum Solved Problems Supplementary ProblemsChapter 15 Curve Sketching.

Concavity. Symmetry. Concavity Points of Inflection Vertical Asymptotes Horizontal Asymptotes Symmetry Inverse Functions and Symmetry Even and Odd Functions Hints for Sketching the Graph G of y = f (x) Solved Problems Supplementary ProblemsChapter 16 Review of Trigonometry Angle Measure Directed Angles Sine and Cosine Functions Solved Problems Supplementary ProblemsChapter 17 Differentiation of Trigonometric Functions Continuity of cos x and sin x Graph of sin x Graph of cos x Other Trigonometric Functions Derivatives Other Relationships Graph of y = tan x Graph of y = sec x Angles Between Curves Solved Problems Supplementary ProblemsChapter 18 Inverse Trigonometric Functions The Derivative of sin−1 x The Inverse Cosine Function The Inverse Tangent Function Solved Problems Supplementary ProblemsChapter 19 Rectilinear and Circular Motion Rectilinear Motion Motion Under the Influence of Gravity Circular Motion Solved Problems Supplementary ProblemsChapter 20 Related Rates Solved Problems Supplementary ProblemsChapter 21 Differentials. Newton''s Method. The Differential Definition Newton''s Method Solved Problems Supplementary ProblemsChapter 22 Antiderivatives Laws for Antiderivatives Solved Problems Supplementary ProblemsChapter 23 The Definite Integral. Area Under a Curve. Sigma Notation Area Under a Curve Properties of the Definite Integral Solved Problems Supplementary ProblemsChapter 24 The Fundamental Theorem of Calculus Mean Value Theorem for Integrals Average Value of a Function on a Closed Interval Fundamental Theorem of Calculus Change of Variable in a Definite Integral Solved Problems Supplementary ProblemsChapter 25 The Natural Logarithm The Natural Logarithm Definition Properties of the Natural Logarithm Solved Problems Supplementary ProblemsChapter 26 Exponential and Logarithmic Functions Definition Properties of ex The General Exponential Function General Logarithmic Functions Solved Problems Supplementary ProblemsChapter 27 L''Hôpital''s Rule L''Hôpital''s Rule Indeterminate Type 0 · ∞ Indeterminate Type ∞ − ∞ Indeterminate Types 00, ∞0, and 1∞ Solved Problems Supplementary ProblemsChapter 28 Exponential Growth and Decay Half-Life Solved Problems Supplementary ProblemsChapter 29 Applications of Integration I: Area and Arc Length Area Between a Curve and the Y-Axis Areas Between Curves Arc Length Solved Problems Supplementary ProblemsChapter 30 Applications of Integration II: Volume Disk Formula Washer Method Cylindrical Shell Method Difference of Shells Formula Cross-Section Formula (Slicing Formula) Solved Problems Supplementary ProblemsChapter 31 Techniques of Integration I: Integration by Parts Solved Problems Supplementary ProblemsChapter 32 Techniques of Integration II: Trigonometric Integrands and Trigonometric Substitutions Trigonometric Integrands Trigonometric Substitutions Solved Problems Supplementary ProblemsChapter 33 Techniques of Integration III: Integration by Partial Fractions Method of Partial Fractions Solved Problems Supplementary ProblemsChapter 34 Techniques of Integration IV: Miscellaneous Substitutions Solved Problems Supplementary ProblemsChapter 35 Improper Integrals Infinite Limits of Integration Discontinuities of the Integrand Solved Problems Supplementary ProblemsChapter 36 Applications of Integration III: Area of a Surface of Revolution Solved Problems Supplementary ProblemsChapter 37 Parametric Representation of Curves Parametric Equations Arc Length for a Parametric Curve Solved Problems Supplementary ProblemsChapter 38 Curvature Derivative of Arc Length Curvature The Radius of Curvature The Circle of Curvature The Center of Curvature The Evolute Solved Problems Supplementary ProblemsChapter 39 Plane Vectors Scalars and Vectors Sum and Difference of Two Vectors Components of a Vector Scalar Product (or Dot Product) Scalar and Vector Projections Differentiation of Vector Functions Solved Problems Supplementary ProblemsChapter 40 Curvilinear Motion Velocity in Curvilinear Motion Acceleration in Curvilinear Motion Tangential and Normal Components of Acceleration Solved Problems Supplementary ProblemsChapter 41 Polar Coordinates Polar and Rectangular Coordinates Some Typical Polar Curves.