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Precalculus: A Prelude to Calculus

Publisher: 
John Wiley
Number of Pages: 
540
Price: 
44.95
ISBN: 
9780471614432

For the review of Precalculus, the recent recommendations from the Committee on the Undergraduate Program in Mathematics (CUPM) are used as an outline. The headings below are the CUPM recommendations; each is followed by my attempt to assess the extent to which the book conforms to them.

Present key ideas and concepts from a variety of perspectives

Chapter 4 (randomly selected), Area, e, and the Natural Logarithm, includes five sections and 66 pages. Of the 66 pages, twenty-seven pages contain graphs. The following are the section number and the amount of examples in each sections: {(1, 7), (2, 5), (3, 2), (4, 0), (5, 4)}. Definitions, properties and concepts are boxed in and colored to highlight their importance throughout the text.

Promote awareness of connections to other subjects and strengthen each student’s ability to apply the course material to these subjects

Looking through the chapter review questions for exercises that include context, the following amounts are per chapter (including chapter 0) out of the total problems in the review were found: {0 out of 20, 0 out of 30, 0 out of 30, 7 out of 36, 5 out of 30, 0 out of 50, 1 out of 41 and 0 out of 14}.

Employ a broad range of instructional techniques, and require students to confront, explore, and communicate important ideas of modern mathematics and the uses of mathematics in society. Students need more classroom experiences in which they learn to think, to do, to analyze – not just memorize and reproduce theories or algorithms

Included in each section of every chapter are exercises (and worked solutions) and problems. The problems tend to be open-ended and need explanations, not just computation.

Understand and respond to the impact of computer technology on course content and instructional techniques

A calculator icon is used throughout the exercises and problems to delineate the questions that need a calculator to work through or to estimate an answer.

At first glance, I was really excited by this text. I like the idea of having open-ended problems for the students to struggle with. But very few of the open-ended problems incorporate real-world applications. So, in order to utilize this text and teach with connections to other subjects, I would need to supplement it. Furthermore, when teaching precalculus I emphasize the use of multiple representations of functions (graphic, numeric, symbolic, and verbal) by using a graphing calculator. Therefore, more supplementation would be needed.


Jane Ries Cushman currently works at Buffalo State College in Buffalo, NY as an assistant professor. She received her doctorate at The University of Texas at Austin in August 2006. She is editor of the Association of Mathematics Teachers of New York State Newsletter and she is the chair of the Association of Mathematics Teacher Educators Affiliate’s Connection Committee. Her research interests include Inquiry-Based Learning, Problem-Solving and Functions-Based Approach to Algebra.

Date Received: 
Friday, January 18, 2008
Reviewable: 
Yes
Include In BLL Rating: 
No
Sheldon Axler
Publication Date: 
2008
Format: 
Paperback
Category: 
Textbook
Jane Ries Cushman
04/30/2008
About the Author v
Preface to the Instructor xiii
Acknowledgments xviii
Preface to the Student xx
0 The Real Numbers 1
0.1 The Real Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
• Construction of the Real Line. . . . . . . . . . . . . . . . . . 2
• Is Every Real Number Rational?. . . . . . . . . . . . . . . . . 3
• Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
0.2 Algebra of the Real Numbers . . . . . . . . . . . . . . . . . . . . . 7
• Commutativity and Associativity . . . . . . . . . . . . . . . . 7
• The Order of Algebraic Operations . . . . . . . . . . . . . . . 8
• The Distributive Property. . . . . . . . . . . . . . . . . . . . 10
• Additive Inverses and Subtraction . . . . . . . . . . . . . . . 11
• Multiplicative Inverses and Division . . . . . . . . . . . . . . 12
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 13
0.3 Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
• Positive and Negative Numbers. . . . . . . . . . . . . . . . . 18
• Lesser and Greater . . . . . . . . . . . . . . . . . . . . . . . 19
• Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
• Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . 24
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 26
Chapter Summary and Chapter Review Questions . . . . . . . . . . . 31
1 Functions and Their Graphs 32
1.1 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
• Examples of Functions . . . . . . . . . . . . . . . . . . . . . 33
• Equality of Functions . . . . . . . . . . . . . . . . . . . . . . 34
• The Domain of a Function . . . . . . . . . . . . . . . . . . . 35
• Functions via Tables . . . . . . . . . . . . . . . . . . . . . . 36
• The Range of a Function . . . . . . . . . . . . . . . . . . . . 37
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 39
1.2 The Coordinate Plane and Graphs . . . . . . . . . . . . . . . . . . 44
• The Coordinate Plane. . . . . . . . . . . . . . . . . . . . . . 44
• The Graph of a Function . . . . . . . . . . . . . . . . . . . . 46
vi
Contents vii
• Determining a Function from Its Graph . . . . . . . . . . . . 47
• Which Sets Are Graphs? . . . . . . . . . . . . . . . . . . . . 49
• Determining the Range of a Function from Its Graph. . . . . . 50
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 51
1.3 Function Transformations and Graphs . . . . . . . . . . . . . . . 59
• Shifting a Graph Up or Down . . . . . . . . . . . . . . . . . . 59
• Shifting a Graph Right or Left . . . . . . . . . . . . . . . . . 61
• Stretching a Graph Vertically or Horizontally. . . . . . . . . . 62
• Reflecting a Graph Vertically or Horizontally. . . . . . . . . . 64
• Even and Odd Functions . . . . . . . . . . . . . . . . . . . . 65
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 67
1.4 Composition of Functions . . . . . . . . . . . . . . . . . . . . . . . 77
• Definition of Composition . . . . . . . . . . . . . . . . . . . 77
• Order Matters in Composition . . . . . . . . . . . . . . . . . 78
• The Identity Function. . . . . . . . . . . . . . . . . . . . . . 79
• Decomposing Functions . . . . . . . . . . . . . . . . . . . . 79
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 80
1.5 Inverse Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
• Examples of Inverse Functions . . . . . . . . . . . . . . . . . 85
• One-to-one Functions. . . . . . . . . . . . . . . . . . . . . . 86
• The Definition of an Inverse Function . . . . . . . . . . . . . 87
• Finding a Formula for an Inverse Function . . . . . . . . . . . 89
• The Domain and Range of an Inverse Function. . . . . . . . . 89
• The Composition of a Function and Its Inverse. . . . . . . . . 90
• Comments about Notation . . . . . . . . . . . . . . . . . . . 92
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 93
1.6 A Graphical Approach to Inverse Functions . . . . . . . . . . . . 99
• The Graph of an Inverse Function . . . . . . . . . . . . . . . 99
• Inverse Functions via Tables . . . . . . . . . . . . . . . . . . 101
• Graphical Interpretation of One-to-One. . . . . . . . . . . . . 101
• Increasing and Decreasing Functions. . . . . . . . . . . . . . 102
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 105
Chapter Summary and Chapter Review Questions . . . . . . . . . . . 109
2 Linear, Quadratic, Polynomial, and Rational Functions 111
2.1 Linear Functions and Lines . . . . . . . . . . . . . . . . . . . . . . 112
• Slope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
• The Equation of a Line . . . . . . . . . . . . . . . . . . . . . 113
• Parallel Lines . . . . . . . . . . . . . . . . . . . . . . . . . . 116
• Perpendicular Lines. . . . . . . . . . . . . . . . . . . . . . . 119
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 121
2.2 Quadratic Functions and Parabolas . . . . . . . . . . . . . . . . . 129
• The Vertex of a Parabola . . . . . . . . . . . . . . . . . . . . 129
viii Contents
• Completing the Square . . . . . . . . . . . . . . . . . . . . . 131
• The Quadratic Formula . . . . . . . . . . . . . . . . . . . . . 133
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 135
2.3 Integer Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
• Exponentiation by Positive Integers . . . . . . . . . . . . . . 141
• Properties of Exponentiation . . . . . . . . . . . . . . . . . . 142
• Defining x0 . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
• Exponentiation by Negative Integers . . . . . . . . . . . . . . 144
• Manipulations with Powers . . . . . . . . . . . . . . . . . . . 145
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 147
2.4 Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
• The Degree of a Polynomial. . . . . . . . . . . . . . . . . . . 153
• The Algebra of Polynomials . . . . . . . . . . . . . . . . . . 155
• Zeros and Factorization of Polynomials . . . . . . . . . . . . 156
• The Behavior of a Polynomial Near ±∞. . . . . . . . . . . . . 158
• Graphs of Polynomials . . . . . . . . . . . . . . . . . . . . . 161
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 163
2.5 Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
• Ratios of Polynomials. . . . . . . . . . . . . . . . . . . . . . 168
• The Algebra of Rational Functions . . . . . . . . . . . . . . . 169
• Division of Polynomials. . . . . . . . . . . . . . . . . . . . . 170
• The Behavior of a Rational Function Near ±∞ . . . . . . . . . 173
• Graphs of Rational Functions. . . . . . . . . . . . . . . . . . 175
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 176
Chapter Summary and Chapter Review Questions . . . . . . . . . . . 183
3 Exponents and Logarithms 185
3.1 Rational and Real Exponents . . . . . . . . . . . . . . . . . . . . . 186
• Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
• Rational Exponents . . . . . . . . . . . . . . . . . . . . . . . 189
• Real Exponents . . . . . . . . . . . . . . . . . . . . . . . . . 191
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 193
3.2 Logarithms as Inverses of Exponentiation . . . . . . . . . . . . . 199
• Logarithms Base 2 . . . . . . . . . . . . . . . . . . . . . . . 199
• Logarithms with Arbitrary Base. . . . . . . . . . . . . . . . . 200
• Change of Base . . . . . . . . . . . . . . . . . . . . . . . . . 202
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 204
3.3 Algebraic Properties of Logarithms . . . . . . . . . . . . . . . . . 209
• Logarithm of a Product . . . . . . . . . . . . . . . . . . . . . 209
• Logarithm of a Quotient . . . . . . . . . . . . . . . . . . . . 210
• Common Logarithms and the Number of Digits . . . . . . . . 211
• Logarithm of a Power. . . . . . . . . . . . . . . . . . . . . . 212
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 213
Contents ix
3.4 Exponential Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
• Functions with Exponential Growth . . . . . . . . . . . . . . 220
• Population Growth . . . . . . . . . . . . . . . . . . . . . . . 222
• Compound Interest. . . . . . . . . . . . . . . . . . . . . . . 224
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 228
3.5 Additional Applications of Exponents and Logarithms . . . . . 234
• Radioactive Decay and Half-Life . . . . . . . . . . . . . . . . 234
• Earthquakes and the Richter Scale . . . . . . . . . . . . . . . 236
• Sound Intensity and Decibels. . . . . . . . . . . . . . . . . . 238
• Star Brightness and Apparent Magnitude. . . . . . . . . . . . 239
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 241
Chapter Summary and Chapter Review Questions . . . . . . . . . . . 247
4 Area, e, and the Natural Logarithm 249
4.1 Distance, Length, and Circles . . . . . . . . . . . . . . . . . . . . . 250
• Distance between Two Points. . . . . . . . . . . . . . . . . . 250
• Midpoints. . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
• Distance between a Point and a Line . . . . . . . . . . . . . . 253
• Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
• Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 257
4.2 Areas of Simple Regions . . . . . . . . . . . . . . . . . . . . . . . . 263
• Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
• Rectangles . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
• Parallelograms . . . . . . . . . . . . . . . . . . . . . . . . . 264
• Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
• Trapezoids . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
• Stretching. . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
• Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
• Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 272
4.3 e and the Natural Logarithm . . . . . . . . . . . . . . . . . . . . . . 280
• Estimating Area Using Rectangles . . . . . . . . . . . . . . . 280
• Defining e. . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
• Defining the Natural Logarithm. . . . . . . . . . . . . . . . . 284
• Properties of the Exponential Function and ln . . . . . . . . . 285
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 287
4.4 Approximations with e and ln. . . . . . . . . . . . . . . . . . . . . 294
• Approximations of the Natural Logarithm . . . . . . . . . . . 294
• Inequalities with the Natural Logarithm . . . . . . . . . . . . 295
• Approximations with the Exponential Function . . . . . . . . 296
• An Area Formula . . . . . . . . . . . . . . . . . . . . . . . . 297
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 300
x Contents
4.5 Exponential Growth Revisited . . . . . . . . . . . . . . . . . . . . . 304
• Continuously Compounded Interest . . . . . . . . . . . . . . 304
• Continuous Growth Rates . . . . . . . . . . . . . . . . . . . 305
• Doubling Your Money. . . . . . . . . . . . . . . . . . . . . . 306
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 308
Chapter Summary and Chapter Review Questions . . . . . . . . . . . 313
5 Trigonometric Functions 315
5.1 The Unit Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316
• The Equation of the Unit Circle. . . . . . . . . . . . . . . . . 316
• Angles in the Unit Circle . . . . . . . . . . . . . . . . . . . . 317
• Negative Angles. . . . . . . . . . . . . . . . . . . . . . . . . 319
• Angles Greater Than 360◦ . . . . . . . . . . . . . . . . . . . 320
• Length of a Circular Arc . . . . . . . . . . . . . . . . . . . . 321
• Special Points on the Unit Circle . . . . . . . . . . . . . . . . 322
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 323
5.2 Radians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
• A Natural Unit of Measurement for Angles . . . . . . . . . . . 329
• Negative Angles. . . . . . . . . . . . . . . . . . . . . . . . . 332
• Angles Greater Than 2π . . . . . . . . . . . . . . . . . . . . 333
• Length of a Circular Arc . . . . . . . . . . . . . . . . . . . . 334
• Area of a Slice . . . . . . . . . . . . . . . . . . . . . . . . . 334
• Special Points on the Unit Circle . . . . . . . . . . . . . . . . 335
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 336
5.3 Cosine and Sine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
• Definition of Cosine and Sine. . . . . . . . . . . . . . . . . . 341
• Cosine and Sine of Special Angles . . . . . . . . . . . . . . . 343
• The Signs of Cosine and Sine . . . . . . . . . . . . . . . . . . 344
• The Key Equation Connecting Cosine and Sine . . . . . . . . . 346
• The Graphs of Cosine and Sine . . . . . . . . . . . . . . . . . 347
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 350
5.4 More Trigonometric Functions . . . . . . . . . . . . . . . . . . . . 355
• Definition of Tangent. . . . . . . . . . . . . . . . . . . . . . 355
• Tangent of Special Angles . . . . . . . . . . . . . . . . . . . 356
• The Sign of Tangent . . . . . . . . . . . . . . . . . . . . . . 357
• Connections between Cosine, Sine, and Tangent . . . . . . . . 358
• The Graph of Tangent . . . . . . . . . . . . . . . . . . . . . 358
• Three More Trigonometric Functions. . . . . . . . . . . . . . 360
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 361
5.5 Trigonometry in Right Triangles . . . . . . . . . . . . . . . . . . . 367
• Trigonometric Functions via Right Triangles . . . . . . . . . . 367
• Two Sides of a Right Triangle. . . . . . . . . . . . . . . . . . 369
• One Side and One Angle of a Right Triangle . . . . . . . . . . 370
Contents xi
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 371
5.6 Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . 377
• The Relationship Between Cosine and Sine . . . . . . . . . . . 377
• Trigonometric Identities for the Negative of an Angle . . . . . 379
• Trigonometric Identities with π2
. . . . . . . . . . . . . . . . 380
• Trigonometric Identities Involving a Multiple of π . . . . . . . 382
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 386
5.7 Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . . . 392
• The Arccosine Function. . . . . . . . . . . . . . . . . . . . . 392
• The Arcsine Function. . . . . . . . . . . . . . . . . . . . . . 395
• The Arctangent Function . . . . . . . . . . . . . . . . . . . . 397
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 400
5.8 Inverse Trigonometric Identities . . . . . . . . . . . . . . . . . . . 403
• The Arccosine, Arcsine, and Arctangent of −t:
Graphical Approach . . . . . . . . . . . . . . . . . . . . . 403
• The Arccosine, Arcsine, and Arctangent of −t:
Algebraic Approach . . . . . . . . . . . . . . . . . . . . . 405
• Arccosine Plus Arcsine . . . . . . . . . . . . . . . . . . . . . 406
• The Arctangent of 1t
. . . . . . . . . . . . . . . . . . . . . . 406
• Composition of Trigonometric Functions and Their Inverses. . 407
• More Compositions with Inverse Trigonometric Functions . . . 408
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 411
Chapter Summary and Chapter Review Questions . . . . . . . . . . . 415
6 Applications of Trigonometry 417
6.1 Using Trigonometry to Compute Area . . . . . . . . . . . . . . . . 418
• The Area of a Triangle via Trigonometry . . . . . . . . . . . . 418
• Ambiguous Angles . . . . . . . . . . . . . . . . . . . . . . . 419
• The Area of a Parallelogram via Trigonometry . . . . . . . . . 421
• The Area of a Polygon . . . . . . . . . . . . . . . . . . . . . 422
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 423
6.2 The Law of Sines and the Law of Cosines . . . . . . . . . . . . . . 429
• The Law of Sines . . . . . . . . . . . . . . . . . . . . . . . . 429
• Using the Law of Sines . . . . . . . . . . . . . . . . . . . . . 430
• The Law of Cosines . . . . . . . . . . . . . . . . . . . . . . . 432
• Using the Law of Cosines . . . . . . . . . . . . . . . . . . . . 433
• When to Use Which Law . . . . . . . . . . . . . . . . . . . . 435
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 436
6.3 Double-Angle and Half-Angle Formulas . . . . . . . . . . . . . . . 444
• The Cosine of 2θ . . . . . . . . . . . . . . . . . . . . . . . . 444
• The Sine of 2θ . . . . . . . . . . . . . . . . . . . . . . . . . 445
• The Tangent of 2θ . . . . . . . . . . . . . . . . . . . . . . . 446
• The Cosine and Sine of θ2
. . . . . . . . . . . . . . . . . . . . 447
xii Contents
• The Tangent of θ2
. . . . . . . . . . . . . . . . . . . . . . . . 449
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 450
6.4 Addition and Subtraction Formulas . . . . . . . . . . . . . . . . . 458
• The Cosine of a Sum and Difference . . . . . . . . . . . . . . 458
• The Sine of a Sum and Difference. . . . . . . . . . . . . . . . 460
• The Tangent of a Sum and Difference . . . . . . . . . . . . . 461
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 462
6.5 Transformations of Trigonometric Functions . . . . . . . . . . . 468
• Amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . 468
• Period. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
• Phase Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 475
6.6 Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
• Defining Polar Coordinates . . . . . . . . . . . . . . . . . . . 484
• Converting from Polar to Rectangular Coordinates. . . . . . . 485
• Converting from Rectangular to Polar Coordinates. . . . . . . 486
• Graphs of Polar Equations . . . . . . . . . . . . . . . . . . . 490
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 492
Chapter Summary and Chapter Review Questions . . . . . . . . . . . 495
7 Sequences, Series, and Limits 497
7.1 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
• Introduction to Sequences . . . . . . . . . . . . . . . . . . . 498
• Arithmetic Sequences. . . . . . . . . . . . . . . . . . . . . . 500
• Geometric Sequences . . . . . . . . . . . . . . . . . . . . . . 501
• Recursive Sequences . . . . . . . . . . . . . . . . . . . . . . 503
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 505
7.2 Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512
• Sums of Sequences . . . . . . . . . . . . . . . . . . . . . . . 512
• Arithmetic Series . . . . . . . . . . . . . . . . . . . . . . . . 512
• Geometric Series . . . . . . . . . . . . . . . . . . . . . . . . 514
• Summation Notation . . . . . . . . . . . . . . . . . . . . . . 516
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 517
7.3 Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522
• Introduction to Limits . . . . . . . . . . . . . . . . . . . . . 522
• Infinite Series. . . . . . . . . . . . . . . . . . . . . . . . . . 526
• Decimals as Infinite Series . . . . . . . . . . . . . . . . . . . 528
• Special Infinite Series . . . . . . . . . . . . . . . . . . . . . . 530
• Exercises, Problems, and Worked-out Solutions . . . . . . . . 531
Chapter Summary and Chapter Review Questions . . . . . . . . . . . 535
Index of Definitions 536
Index of Boxed Items 538
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