1.1 Precalculus Review I 1

Applied Calculus for the Managerial, Life, and Social Sciences A Brief Approach 10e Soo Tan

(Solutions Manual All Chapters) 1 / 4

CONTENTS

CHAPTER 1 Preliminaries 1 1.1 Precalculus Review I 1 1.2 Precalculus Review II 8 1.3 The Cartesian Coordinate System 15 1.4 Straight Lines 20 Chapter 1 Review 29 Chapter 1 Before Moving On 34 Chapter 1 Explore & Discuss 35 Chapter 1 Exploring with Technology 36 CHAPTER 2 Functions, Limits, and the Derivative 37 2.1 Functions and Their Graphs 37 2.2 The Algebra of Functions 49 2.3 Functions and Mathematical Models 55 2.4 Limits 67 2.5 One-Sided Limits and Continuity 76 2.6 The Derivative 85 Chapter 2 Review 97 Chapter 2 Before Moving On 105 Chapter 2 Explore & Discuss 106 Chapter 2 Exploring with Technology 108 CHAPTER 3 Differentiation 113 3.1 Basic Rules of Differentiation 1133.2 The Product and Quotient Rules 121 3.3 The Chain Rule 132 3.4 Marginal Functions in Economics 143 3.5 Higher-Order Derivatives 150 3.6 Implicit Differentiation and Related Rates 156 3.7 Differentials 164 Chapter 3 Review 170 Chapter 3 Before Moving On 179 v 2 / 4

vi CONTENTS Chapter 3 Explore & Discuss 180 Chapter 3 Exploring with Technology 181 CHAPTER 4 Applications of the Derivative 183 4.1 Applications of the First Derivative 183 4.2 Applications of the Second Derivative 197 4.3 Curve Sketching 210 4.4 Optimization I 231 4.5 Optimization II 245 Chapter 4 Review 253 Chapter 4 Before Moving On 267 Chapter 4 Explore & Discuss 268 Chapter 4 Exploring with Technology 270 CHAPTER 5 Exponential and Logarithmic Functions 273 5.1 Exponential Functions 273 5.2 Logarithmic Functions 279 5.3 Compound Interest 284 5.4 Differentiation of Exponential Functions 290 5.5 Differentiation of Logarithmic Functions 303 5.6 Exponential Functions as Mathematical Models 314 Chapter 5 Review 322 Chapter 5 Before Moving On 329 Chapter 5 Explore & Discuss 330 Chapter 5 Exploring with Technology 330 CHAPTER 6 Integration 333 6.1 Antiderivatives and the Rules of Integration 333 6.2 Integration by Substitution 340 6.3 Area and the Definite Integral 347 6.4 The Fundamental Theorem of Calculus 350 6.5 Evaluating Definite Integrals 356 6.6 Area Between Two Curves 363 3 / 4

CONTENTS vii 6.7 Applications of the Definite Integral to Business and Economics 373 Chapter 6 Review 378 Chapter 6 Before Moving On 385 Chapter 6 Explore & Discuss 386 Chapter 6 Exploring with Technology 388 CHAPTER 7 Additional Topics in Integration 391 7.1 Integration by Parts 391 7.2 Integration Using Tables of Integrals 398 7.3 Numerical Integration 404 7.4 Improper Integrals 414 7.5 Applications of Calculus to Probability 419 Chapter 7 Review 426 Chapter 7 Before Moving On 431 Chapter 7 Explore & Discuss 431 Chapter 7 Exploring with Technology 433 CHAPTER 8 Calculus of Several Variables 435 8.1 Functions of Several Variables 4358.2 Partial Derivatives 4418.3 Maxima and Minima of Functions of Several Variables 4498.4 The Method of Least Squares 459 8.5 Constrained Maxima and Minima and the Method of Lagrange Multipliers 467 8.6 Double Integrals 478 Chapter 8 Review 482 Chapter 8 Before Moving On 491 Chapter 8 Explore & Discuss 491 Chapter 8 Exploring with Technology 494

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