Instructor’s Solutions Manual
for
Applied Calculus for the Managerial, Life, and Social Sciences Enhanced Edition
Prepared by
Petra Menz
Simon Fraser University
Dan Ashlock
University of Guelph
Instructor’s Solutions Manual for Applied Calculus for the Managerial, Life, and Social Sciences, Enhanced Edition Prepared by Petra Menz and Dan Ashlock Copyright © 2009 by Nelson Education Ltd. ALL RIGHTS RESERVED. No part of this work covered by the copyright herein may be reproduced, transcribed, or used in any form or by any means—graphic, electronic, or mechanical, including photocopying, recording, taping, Web distribution, or
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CONTENTS CHAPTER 1
Preliminaries 1.1
Precalculus Review I.........................................................................1
1.2
Precalculus Review II......................................................................11
1.3
The Cartesian Coordinate System ...................................................19
1.4
Straight Lines ..................................................................................25
Chapter 1 Review Exercises......................................................................38
CHAPTER 2
Functions 2.1
Functions and Their Graphs ...........................................................46
2.2
Transformations of Functions .........................................................61
2.3
Polynomial Functions......................................................................69
2.4
Rational and Power Functions.........................................................74
2.5
Absolute Value Functions ...............................................................80
2.6
The Algebra of Functions................................................................89
2.7
The Inverse of a Function................................................................96
2.8
Functions and Mathematical Models ............................................102
Chapter 2 Review Exercises....................................................................114
CHAPTER 3
Limits and the Derivative 3.1
Limits ............................................................................................132
3.2
One-Sided Limits and Continuity .................................................142
3.3
The Derivative...............................................................................153
3.4
Basic Rules of Differentiation.......................................................170
3.5
The Product and Quotient Rules ...................................................180
3.6
The Chain Rule .............................................................................195
Chapter 3 Review Exercises....................................................................211
CHAPTER 4
Differentiation 4.1
Marginal Functions in Economics.................................................229
4.2
Visual Differentiation....................................................................238
4.3
Higher-Order Derivatives..............................................................246
4.4
Implicit Differentiation and Related Rates....................................253
4.5
Differentials and Linear Approximation....................................... 267
4.6
The Newton-Raphson Method...................................................... 275
Chapter 4 Review Exercises ................................................................... 283
CHAPTER 5
Exponential and Logarithmic Functions 5.1
Exponential Functions .................................................................. 292
5.2
Logarithmic Functions.................................................................. 298
5.3
Differentiation of Exponential Functions ..................................... 308
5.4
Differentiation of Logarithmic Functions..................................... 318
5.5
Exponential Functions as Mathematical Models .......................... 327
Chapter 5 Review Exercises ................................................................... 334
CHAPTER 6
Trigonometric Functions 6.1
Measurement of Angles ................................................................ 345
6.2
The Trigonometric Functions ....................................................... 347
6.3
Inverse Trigonometric Functions.................................................. 355
6.4
Differentiation Rules..................................................................... 358
Chapter 6 Review Exercises ................................................................... 366
CHAPTER 7
Applications of the Derivative 7.1
Applications of the First Derivative.............................................. 377
7.2
Applications of the Second Derivative ......................................... 399
7.3
Curve Sketching............................................................................ 420
7.4
Optimization I ............................................................................... 459
7.5
Optimization II.............................................................................. 482
7.6
L’Hôpital’s Rule: Indeterminate Forms........................................ 493
Chapter 7 Review Exercises ................................................................... 504
CHAPTER 8
Integration 8.1
Anitderivatives and the Rules of Integration ................................ 546
8.2
Integration by Substitution ........................................................... 559
8.3
Area and the Definite Integral....................................................... 574
8.4
The Fundamental Theorem of Calculus........................................ 579
8.5
Evaluating Definite Integrals ........................................................ 587
8.6
Area between Two Curves ............................................................605
8.7
Applications of the Definite Integral to Business and Economics ..............................................................................623
8.8
Volumes of Solids of Revolution ..................................................628
Chapter 8 Review Exercises....................................................................636
CHAPTER 9
Additional Topics in Integration 9.1
Integration by Parts .......................................................................655
9.2
Integration by Partial Fractions .....................................................672
9.3
Integration Using Tables of Integrals............................................695
9.4
Numerical Integration ...................................................................706
9.5
Improper Integrals .........................................................................727
Chapter 9 Review Exercises....................................................................741
CHAPTER 10
Calculus of Several Variables 10.1 Functions of Several Variables .....................................................756 10.2 Partial Derivatives .........................................................................761 10.3 Maxima and Minima of Functions of Several Variables...............775 10.4 The Method of Least Squares........................................................792 10.5 Constrained Maxima and Minima and the Method of Lagrange Multipliers ....................................................................................806 10.6 Total Differentials .........................................................................817 10.7 Double Integrals ............................................................................822 10.8 Applications of Double Integrals ..................................................826 Chapter 10 Review Exercises..................................................................831
CHAPTER 11
Differential Equations 11.1 Differential Equations ...................................................................847 11.2 Separation of Variables .................................................................853 11.3 Applications of Separable Differential Equations.........................863 11.4 Linear Differential Equations........................................................871 11.5 Approximate Solutions of Differential Equations.........................877 Chapter 11 Review Exercises .................................................................887