INSTRUCTOR
SOLUTIONS
MANUAL
INSTRUCTOR
SOLUTIONS
MANUAL
TABLE OF CONTENTS
1 Functions 1
1.1 Functions and Their Graphs 1
1.2 Combining Functions; Shifting and Scaling Graphs 8
1.3 Trigonometric Functions 18
1.4 Graphing with Software 26
1.5 Exponential Functions 31
1.6 Inverse Functions and Logarithms 34
Practice Exercises 43
Additional and Advanced Exercises 52
2 Limits and Continuity 59
2.1 Rates of Change and Tangents to Curves 59
2.2 Limit of a Function and Limit Laws 62
2.3 The Precise Definition of a Limit 73
2.4 One-Sided Limits 81
2.5 Continuity 86
2.6 Limits Involving Infinity; Asymptotes of Graphs 92
Practice Exercises 102
Additional and Advanced Exercises 108
3 Differentiation 115
3.1 Tangents and the Derivative at a Point 115
3.2 The Derivative as a Function 121
3.3 Differentiation Rules 131
3.4 The Derivative as a Rate of Change 138
3.5 Derivatives of Trigonometric Functions 144
3.6 The Chain Rule 152
3.7 Implicit Differentiation 162
3.8 Derivatives of Inverse Functions and Logarithms 170
3.9 Inverse Trigonometric Functions 180
3.10 Related Rates 186
3.11 Linearization and Differentials 192
Practice Exercises 199
Additional and Advanced Exercises 214
