| 1.1.1. | The Hyperbolic Functions | |
| 1.1.2. | The Reciprocal Hyperbolic Functions | |
| 1.1.3. | Solving Equations Containing Hyperbolic Functions | |
| 1.1.4. | Graphs of the Hyperbolic Functions | |
| 1.1.5. | Graphs of the Reciprocal Hyperbolic Functions | |
| 1.1.6. | The Inverse Hyperbolic Functions |
| 2.2.1. | The Finite Limit of a Function | |
| 2.2.2. | The Left and Right-Sided Limits of a Function | |
| 2.2.3. | Finding the Existence of a Limit Using One-Sided Limits | |
| 2.2.4. | Limits at Infinity from Graphs | |
| 2.2.5. | Infinite Limits from Graphs |
| 2.3.1. | Limits of Power Functions, and the Constant Rule for Limits | |
| 2.3.2. | The Sum Rule for Limits | |
| 2.3.3. | The Product and Quotient Rules for Limits | |
| 2.3.4. | The Power and Root Rules for Limits |
| 2.4.1. | Limits at Infinity of Polynomials | |
| 2.4.2. | Limits of Reciprocal Functions | |
| 2.4.3. | Limits of Exponential Functions | |
| 2.4.4. | Limits of Logarithmic Functions | |
| 2.4.5. | Limits of Radical Functions | |
| 2.4.6. | Limits of Trigonometric Functions | |
| 2.4.7. | Limits of Reciprocal Trigonometric Functions | |
| 2.4.8. | Limits of Inverse Trigonometric Functions | |
| 2.4.9. | Limits of Piecewise Functions |
| 2.5.1. | Calculating Limits of Rational Functions by Factoring | |
| 2.5.2. | Limits of Absolute Value Functions | |
| 2.5.3. | Calculating Limits of Radical Functions Using Conjugate Multiplication | |
| 2.5.4. | Calculating Limits Using Trigonometric Identities | |
| 2.5.5. | Limits at Infinity and Horizontal Asymptotes of Rational Functions | |
| 2.5.6. | Evaluating Limits at Infinity by Comparing Relative Magnitudes of Functions | |
| 2.5.7. | Evaluating Limits at Infinity of Radical Functions | |
| 2.5.8. | Vertical Asymptotes of Rational Functions | |
| 2.5.9. | Connecting Infinite Limits and Vertical Asymptotes of Rational Functions |
| 2.6.1. | The Squeeze Theorem | |
| 2.6.2. | Special Limits Involving Sine | |
| 2.6.3. | Evaluating Special Limits Involving Sine Using a Substitution | |
| 2.6.4. | Special Limits Involving Cosine | |
| 2.6.5. | Limits Involving the Exponential Function | |
| 2.6.6. | Further Limits Involving the Exponential Function |
| 3.7.1. | Determining Continuity from Graphs | |
| 3.7.2. | Defining Continuity at a Point | |
| 3.7.3. | Left and Right Continuity | |
| 3.7.4. | Further Continuity of Piecewise Functions | |
| 3.7.5. | Point Discontinuities | |
| 3.7.6. | Jump Discontinuities | |
| 3.7.7. | Discontinuities Due to Vertical Asymptotes | |
| 3.7.8. | Continuity Over an Interval | |
| 3.7.9. | Continuity of Functions | |
| 3.7.10. | The Intermediate Value Theorem |
| 3.8.1. | Removing Point Discontinuities | |
| 3.8.2. | Removing Jump Discontinuities | |
| 3.8.3. | Removing Discontinuities From Rational Functions |
| 4.9.1. | The Average Rate of Change of a Function | |
| 4.9.2. | The Average Rate of Change of a Function over a Varying Interval | |
| 4.9.3. | The Instantaneous Rate of Change of a Function at a Point | |
| 4.9.4. | Defining the Derivative Using Derivative Notation | |
| 4.9.5. | Connecting Differentiability and Continuity | |
| 4.9.6. | The Power Rule for Differentiation | |
| 4.9.7. | The Sum and Constant Multiple Rules for Differentiation | |
| 4.9.8. | Calculating the Slope of a Tangent Line Using Differentiation | |
| 4.9.9. | Calculating the Equation of a Tangent Line Using Differentiation | |
| 4.9.10. | Calculating the Equation of a Normal Line Using Differentiation |
| 4.10.1. | Differentiating Exponential Functions | |
| 4.10.2. | Differentiating Logarithmic Functions | |
| 4.10.3. | Differentiating Trigonometric Functions | |
| 4.10.4. | Differentiating Hyperbolic Functions | |
| 4.10.5. | Differentiating Reciprocal Hyperbolic Functions | |
| 4.10.6. | Second and Higher Order Derivatives | |
| 4.10.7. | The Product Rule for Differentiation | |
| 4.10.8. | The Quotient Rule for Differentiation | |
| 4.10.9. | Differentiating Reciprocal Trigonometric Functions | |
| 4.10.10. | Calculating Derivatives From Data and Tables | |
| 4.10.11. | Calculating Derivatives From Graphs | |
| 4.10.12. | Recognizing Derivatives in Limits |
| 5.11.1. | The Chain Rule for Differentiation | |
| 5.11.2. | The Chain Rule With Exponential Functions | |
| 5.11.3. | The Chain Rule With Logarithmic Functions | |
| 5.11.4. | The Chain Rule With Trigonometric Functions | |
| 5.11.5. | Calculating Derivatives From Data Using the Chain Rule | |
| 5.11.6. | Calculating Derivatives From Graphs Using the Chain Rule | |
| 5.11.7. | Selecting Procedures for Calculating Derivatives |
| 5.12.1. | Implicit Differentiation | |
| 5.12.2. | Calculating Slopes of Circles, Ellipses, and Parabolas | |
| 5.12.3. | Calculating dy/dx Using dx/dy | |
| 5.12.4. | Differentiating Inverse Functions | |
| 5.12.5. | Differentiating an Inverse Function at a Point | |
| 5.12.6. | Differentiating Inverse Trigonometric Functions | |
| 5.12.7. | Differentiating Inverse Reciprocal Trigonometric Functions | |
| 5.12.8. | Differentiating Inverse Hyperbolic Functions | |
| 5.12.9. | Differentiating Inverse Reciprocal Hyperbolic Functions |
| 5.13.1. | Logarithmic Differentiation | |
| 5.13.2. | Further Logarithmic Differentiation |
| 6.14.1. | Interpreting the Meaning of the Derivative in Context | |
| 6.14.2. | Rates of Change in Applied Contexts |
| 6.15.1. | Estimating Derivatives Using a Forward Difference Quotient | |
| 6.15.2. | Estimating Derivatives Using a Backward Difference Quotient | |
| 6.15.3. | Estimating Derivatives Using a Central Difference Quotient |
| 6.16.1. | Introduction to Related Rates | |
| 6.16.2. | Related Rates With Implicit Functions | |
| 6.16.3. | Calculating Related Rates With Circles and Spheres | |
| 6.16.4. | Calculating Related Rates With Squares | |
| 6.16.5. | Calculating Related Rates With Rectangular Solids | |
| 6.16.6. | Calculating Related Rates Using the Pythagorean Theorem | |
| 6.16.7. | Calculating Related Rates Using Similar Triangles | |
| 6.16.8. | Calculating Related Rates Using Trigonometry | |
| 6.16.9. | Calculating Related Rates With Cones |
| 6.17.1. | L'Hopital's Rule | |
| 6.17.2. | L'Hopital's Rule Applied to Tables |
| 7.18.1. | The Mean Value Theorem | |
| 7.18.2. | Global vs. Local Extrema and Critical Points | |
| 7.18.3. | The Extreme Value Theorem | |
| 7.18.4. | Using Differentiation to Calculate Critical Points | |
| 7.18.5. | Determining Intervals on Which a Function Is Increasing or Decreasing | |
| 7.18.6. | Using the First Derivative Test to Classify Local Extrema | |
| 7.18.7. | The Candidates Test | |
| 7.18.8. | Intervals of Concavity | |
| 7.18.9. | Relating Concavity to the Second Derivative | |
| 7.18.10. | Points of Inflection | |
| 7.18.11. | The Second Derivative Test |
| 7.19.1. | Sketching the Derivative of a Function From the Function's Graph | |
| 7.19.2. | Interpreting the Graph of a Function's Derivative | |
| 7.19.3. | Interpreting the Graph of a Function's Derivative: Concavity and Points of Inflection | |
| 7.19.4. | Sketching a Function From the Graph of its Derivative | |
| 7.19.5. | Sketching a Function Given Some Derivative Properties |
| 7.20.1. | Approximating Functions Using Local Linearity and Linearization | |
| 7.20.2. | Approximating the Roots of a Number Using Local Linearity | |
| 7.20.3. | Approximating Trigonometric Functions Using Local Linearity |
| 7.21.1. | Optimization Problems Involving Rectangles | |
| 7.21.2. | Optimization Problems Involving Sectors of Circles | |
| 7.21.3. | Optimization Problems Involving Boxes and Trays | |
| 7.21.4. | Optimization Problems Involving Cylinders | |
| 7.21.5. | Finding Minimum Distances | |
| 7.21.6. | Optimization Problems With Inscribed Shapes | |
| 7.21.7. | Optimization Problems in Economics |
| 7.22.1. | Calculating Velocity for Straight-Line Motion Using Differentiation | |
| 7.22.2. | Calculating Acceleration for Straight-Line Motion Using Differentiation | |
| 7.22.3. | Determining Characteristics of Moving Objects Using Differentiation | |
| 7.22.4. | Newton's Second Law |
| 8.23.1. | The Antiderivative | |
| 8.23.2. | The Constant Multiple Rule for Indefinite Integrals | |
| 8.23.3. | The Sum Rule for Indefinite Integrals | |
| 8.23.4. | Integrating the Reciprocal Function | |
| 8.23.5. | Integrating Exponential Functions | |
| 8.23.6. | Integrating Trigonometric Functions | |
| 8.23.7. | Integration Using Inverse Trigonometric Functions | |
| 8.23.8. | Integrating Hyperbolic Functions | |
| 8.23.9. | Integration Using Inverse Hyperbolic Functions | |
| 8.23.10. | Integration Using Inverse Reciprocal Hyperbolic Functions |
| 8.24.1. | Approximating Areas With the Left Riemann Sum | |
| 8.24.2. | Approximating Areas With the Right Riemann Sum | |
| 8.24.3. | Approximating Areas With the Midpoint Riemann Sum | |
| 8.24.4. | Approximating Areas With the Trapezoidal Rule | |
| 8.24.5. | Left and Right Riemann Sums in Sigma Notation | |
| 8.24.6. | Midpoint and Trapezoidal Rules in Sigma Notation | |
| 8.24.7. | Approximating Areas Under Graphs of Composite Functions |
| 8.25.1. | Defining Definite Integrals Using Left and Right Riemann Sums | |
| 8.25.2. | The Fundamental Theorem of Calculus | |
| 8.25.3. | Applying the Fundamental Theorem of Calculus to Exponential and Trigonometric Functions | |
| 8.25.4. | The Sum and Constant Multiple Rules for Definite Integrals | |
| 8.25.5. | Properties of Definite Integrals Involving the Limits of Integration |
| 8.26.1. | The Area Bounded by a Curve and the X-Axis | |
| 8.26.2. | Evaluating Definite Integrals Using Symmetry | |
| 8.26.3. | Finding the Area Between a Curve and the X-Axis When They Intersect | |
| 8.26.4. | The Area Bounded by a Curve and the Y-Axis | |
| 8.26.5. | Calculating the Definite Integral of a Function Given Its Graph | |
| 8.26.6. | Calculating the Definite Integral of a Function's Derivative Given its Graph | |
| 8.26.7. | Definite Integrals of Piecewise Functions |
| 8.27.1. | The Integral as an Accumulation Function | |
| 8.27.2. | The Second Fundamental Theorem of Calculus | |
| 8.27.3. | Maximizing a Function Using the Graph of Its Derivative | |
| 8.27.4. | Minimizing a Function Using the Graph of its Derivative | |
| 8.27.5. | Further Optimizing Functions Using Graphs of Derivatives |
