Calculus: Single Variable (update)
by Smith, Robert T.; Minton, Roland B.Edition: 2nd
Format: Hardcover
Pub. Date: 2002-08-01
Publisher(s): McGraw-Hill Science/Engineering/Math
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Summary
The wide-ranging debate brought about by the calculus reform movement has had a significant impact on calculus textbooks. In response to many of the questions and concerns surrounding this debate, the authors have written a modern calculus textbook, intended for students majoring in mathematics, physics, chemistry, engineering and related fields. The text is written for the average student -- one who does not already know the subject, whose background is somewhat weak in spots, and who requires a significant motivation to study calculus. The authors follow a relatively standard order of presentation, while integrating technology and thought-provoking exercises throughout the text. Some minor changes have been made in the order of topics to reflect shifts in the importance of certain applications in engineering and science. This text also gives an early introduction to logarithms, exponentials and the trigonometric functions. Wherever practical, concepts are developed from graphical, numerical, and algebraic perspectives (the "Rule of Three") to give students a full understanding of calculus. This text places a significant emphasis on problem solving and presents realistic applications, as well as open-ended problems.
Table of Contents
0 Preliminaries0.1 The Real Numbers and the Cartesian Plane0.2 Lines and Functions0.3 Graphing Calculators and Computer Algebra Systems0.4 Solving Equations0.5 Trigonometric Functions0.6 Exponential and Logarithmic Functions0.7 Transformations of Functions0.8 Preview of Calculus1 Limits and Continuity1.1 The Concept of Limit1.2 Computation of Limits1.3 Continuity and its Consequences1.4 Limits Involving Infinity1.5 Formal Definition of the Limit1.6 Limits and Loss-of-Significance Errors2 Differentiation2.1 Tangent Lines and Velocity2.2 The Derivative2.3 Computation of Derivatives: The Power Rule2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 Derivatives of Exponential and Logarithmic Functions2.7 The Chain Rule2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
0.2 Lines and Functions0.3 Graphing Calculators and Computer Algebra Systems0.4 Solving Equations0.5 Trigonometric Functions0.6 Exponential and Logarithmic Functions0.7 Transformations of Functions0.8 Preview of Calculus1 Limits and Continuity1.1 The Concept of Limit1.2 Computation of Limits1.3 Continuity and its Consequences1.4 Limits Involving Infinity1.5 Formal Definition of the Limit1.6 Limits and Loss-of-Significance Errors2 Differentiation2.1 Tangent Lines and Velocity2.2 The Derivative2.3 Computation of Derivatives: The Power Rule2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 Derivatives of Exponential and Logarithmic Functions2.7 The Chain Rule2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
0.4 Solving Equations0.5 Trigonometric Functions0.6 Exponential and Logarithmic Functions0.7 Transformations of Functions0.8 Preview of Calculus1 Limits and Continuity1.1 The Concept of Limit1.2 Computation of Limits1.3 Continuity and its Consequences1.4 Limits Involving Infinity1.5 Formal Definition of the Limit1.6 Limits and Loss-of-Significance Errors2 Differentiation2.1 Tangent Lines and Velocity2.2 The Derivative2.3 Computation of Derivatives: The Power Rule2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 Derivatives of Exponential and Logarithmic Functions2.7 The Chain Rule2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
0.6 Exponential and Logarithmic Functions0.7 Transformations of Functions0.8 Preview of Calculus1 Limits and Continuity1.1 The Concept of Limit1.2 Computation of Limits1.3 Continuity and its Consequences1.4 Limits Involving Infinity1.5 Formal Definition of the Limit1.6 Limits and Loss-of-Significance Errors2 Differentiation2.1 Tangent Lines and Velocity2.2 The Derivative2.3 Computation of Derivatives: The Power Rule2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 Derivatives of Exponential and Logarithmic Functions2.7 The Chain Rule2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
0.8 Preview of Calculus1 Limits and Continuity1.1 The Concept of Limit1.2 Computation of Limits1.3 Continuity and its Consequences1.4 Limits Involving Infinity1.5 Formal Definition of the Limit1.6 Limits and Loss-of-Significance Errors2 Differentiation2.1 Tangent Lines and Velocity2.2 The Derivative2.3 Computation of Derivatives: The Power Rule2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 Derivatives of Exponential and Logarithmic Functions2.7 The Chain Rule2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
1.1 The Concept of Limit1.2 Computation of Limits1.3 Continuity and its Consequences1.4 Limits Involving Infinity1.5 Formal Definition of the Limit1.6 Limits and Loss-of-Significance Errors2 Differentiation2.1 Tangent Lines and Velocity2.2 The Derivative2.3 Computation of Derivatives: The Power Rule2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 Derivatives of Exponential and Logarithmic Functions2.7 The Chain Rule2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
1.3 Continuity and its Consequences1.4 Limits Involving Infinity1.5 Formal Definition of the Limit1.6 Limits and Loss-of-Significance Errors2 Differentiation2.1 Tangent Lines and Velocity2.2 The Derivative2.3 Computation of Derivatives: The Power Rule2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 Derivatives of Exponential and Logarithmic Functions2.7 The Chain Rule2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
1.5 Formal Definition of the Limit1.6 Limits and Loss-of-Significance Errors2 Differentiation2.1 Tangent Lines and Velocity2.2 The Derivative2.3 Computation of Derivatives: The Power Rule2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 Derivatives of Exponential and Logarithmic Functions2.7 The Chain Rule2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
2 Differentiation2.1 Tangent Lines and Velocity2.2 The Derivative2.3 Computation of Derivatives: The Power Rule2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 Derivatives of Exponential and Logarithmic Functions2.7 The Chain Rule2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
2.2 The Derivative2.3 Computation of Derivatives: The Power Rule2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 Derivatives of Exponential and Logarithmic Functions2.7 The Chain Rule2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
2.4 The Product and Quotient Rules2.5 Derivatives of Trigonometric Functions2.6 Derivatives of Exponential and Logarithmic Functions2.7 The Chain Rule2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
2.6 Derivatives of Exponential and Logarithmic Functions2.7 The Chain Rule2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
2.8 Implicit Differentiation and Related Rates2.9 The Mean Value Theorem3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
3 Applications of Differentiation3.1 Linear Approximations adn L'Hopital's Rule3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
3.2 Newton's Method3.3 Maximum and Minimum Values3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
3.4 Increasing and Decreasing Functions3.5 Concavity3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
3.6 Overview of Curve Sketching3.7 Optimization3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
3.8 Rates of Change in Applications4 Integration4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
4.1 Antiderivatives4.2 Sums and Sigma Notation4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
4.3 Area4.4 The Definite Integral4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
4.5 The Fundamental Theorem of Calculus4.6 Integration by Substitution4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
4.7 Numerical Integration5 Applications of the Definite Integral5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
5.1 Area Between Curves5.2 Volume5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
5.3 Volumes by Cylindrical Shells5.4 Arc Length and Surface Area5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
5.5 Projectile Motion5.6 Work, Moments, and Hydrostatic Force5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
5.7 Probability6 Exponentials, Logarithms, and Other Transcendental Functions6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
6.1 The Natural Logarithm Revisited6.2 Inverse Functions6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
6.3 The Exponential Function Revisited6.4 Growth and Decay Problems6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
6.5 Separable Differential Equations6.6 Euler's Method6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
6.7 The Inverse Trigonometric Functions6.8 The Calculus of the Inverse Trigonometric Functions6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
6.9 The Hyperbolic Functions7 Integration Techniques7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
7.1 Review of Formulas and Techniques7.2 Integration by Parts7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
7.3 Trigonometric Techniques of Integration7.4 Integration of Rational Functions using Partial Fractions7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
7.5 Integration Tables and Computer Algebra Systems7.6 Indeterminate Forms and L'Hopital's Rule7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
7.7 Improper Integrals8 Infinite Series8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
8.1 Sequences of Real Numbers8.2 Infinite Series8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
8.3 The Integral Test and Comparison Tests8.4 Alternating Series8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
8.5 Absolute Convergence and the Ratio Test8.6 Power Series8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
8.7 Taylor Series8.8 Fourier Series9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
9 Parametric Equations and Polar Coordinates9.1 Plane Curves and Parametric Equations9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
9.2 Calculus and Parametric Equations9.3 Arc Length and Surface Area in Parametric Equations9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
9.4 Polar Coordinates9.5 Calculus and Polar Coordinates9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
9.6 Conic Sections9.7 Conic Sections in Polar Coordinates
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