Precalculus : mathematics for calculus : student solutions manual

Contents 5 Ch 1: Fundamentals 11 1.1: Real Numbers 11 1.2: Exponents and Radicals 13 1.3: Algebraic Expressions 16 1.4: Rational Expressions 20 1.5: Equations 24 1.6: Modeling with Equations 28 1.7: Inequalities 33 1.8: Coordinate Geometry 42 1.9: Graphing Calculators; Solving Equations and Inequalities Graphically 53 1.10: Lines 59 1.11: Making Models Using Variation 64 Chapter 1 Review 66 Chapter 1 Test 72 Focus on Modeling: Fitting Lines to Data 75 Ch 2: Functions 79 2.1: What is a Function? 79 2.2 Graphs of Functions 83 2.3: Getting Information from the Graph of a Function 89 2.4: Average Rate of Change of a Function 93 2.5: Transformations of Functions 95 2.6: Combining Functions 101 2.7: One-to-One Functions and Their Inverses 105 Chapter 2 Review 110 Chapter 2 Test 116 Focus on Modeling: Modeling with Functions 117 Ch 3: Polynomial and Rational Functions 123 3.1: Quadratic Functions and Models 123 3.2: Polynomial Functions and Their Graphs 128 3.3: Dividing Polynomials 135 3.4: Real Zeros of Polynomials 139 3.5: Complex Numbers 155 3.6: Complex Zeros and the Fundamental Theorem of Algebra 157 3.7: Rational Functions 162 Chapter 3 Review 170 Chapter 3 Test 178 Focus on Modeling: Fitting Polynomial Curves to Data 180 Ch 4: Exponential and Logarithmic Functions 183 4.1: Exponential Functions 183 4.2: The Natural Exponential Function 187 4.3: Logarithmic Functions 190 4.4: Laws of Logarithms 194 4.5: Exponential and Logarithmic Equations 196 4.6: Modeling with Exponential and Logarithmic Functions 200 Chapter 4 Review 203 Chapter 4 Test 207 Focus on Modeling: Fitting Exponential and Power Curves to Data 208 Cumulative Review Test: Chapters 2, 3, and 4 210 Ch 5: Trigonometric Functions: Unit Circle Approach 213 5.1: The Unit Circle 213 5.2: Trigonometric Functions of Real Numbers 215 5.3: Trigonometric Graphs 217 5.4: More Trigonometric Graphs 223 5.5: Inverse Trigonometric Functions and Their Graphs 226 5.6: Modeling Harmonic Motion 227 Chapter 5 Review 230 Chapter 5 Test 233 Focus on Modeling: Fitting Sinusoidal Curves to Data 234 Ch 6: Trigonometric Functions: Right Triangle Approach 237 6.1: Angle Measure 237 6.2: Trigonometry of Right Triangles 238 6.3: Trigonometric Functions of Angles 241 6.4: Inverse Trigonometric Functions and Triangles 243 6.5: The Law of Sines 245 6.6: The Law of Cosines 247 Chapter 6 Review 249 Chapter 6 Test 252 Focus on Modeling: Surveying 253 Ch 7: Analytic Trigonometry 255 7.1: Trigonometric Identities 255 7.2: Addition and Subtraction Formulas 258 7.3: Double-Angle, Half-Angle, and Product-Sum Formulas 262 7.4: Basic Trigonometric Equations 267 7.5: More Trigonometric Equations 269 Chapter 7 Review 272 Chapter 7 Test 275 Focus on Modeling: Traveling and Standing Waves 276 Cumulative Review Test: Chapters 5, 6, and 7 276 Ch 8: Polar Coordinates and Parametric Equations 279 8.1: Polar Coordinates 279 8.2: Graphs of Polar Equations 281 8.3: Polar Form of Complex Numbers; De Moivre's Theorem 284 8.4: Plane Curves and Parametric Equations 290 Chapter 8 Review 296 Chapter 8 Test 300 Focus on Modeling: The Path of a Projectile 300 Ch 9: Vectors in Two and Three Dimensions 303 9.1: Vectors in Two Dimensions 303 9.2: The Dot Product 306 9.3: Three-Dimensional Coordinate Geometry 308 9.4: Vectors in Three Dimensions 309 9.5: The Cross Product 311 9.6: Equations of Lines and Planes 312 Chapter 9 Review 314 Chapter 9 Test 316 Focus on Modeling: Vector Fields 317 Cumulative Review Test: Chapters 8 and 9 318 Ch 10: Systems of Equations and Inequalities 321 10.1: Systems of Linear Equations in Two Variables 321 10.2: Systems of Linear Equations in Several Variables 324 10.3: Matrices and Systems of Linear Equations 329 10.4: The Algebra of Matrices 334 10.5: Inverses of Matrices and Matrix Equations 338 10.6: Determinants and Cramer's Rule 342 10.7: Partial Fractions 349 10.8: Systems of Nonlinear Equations 354 10.9: Systems of Inequalities 359 Chapter 10 Review 364 Chapter 10 Test 372 Focus on Modeling: Linear Programming 374 Ch 11: Conic Sections 379 11.1: Parabolas 379 11.2: Ellipses 381 11.3: Hyperbolas 384 11.4: Shifted Conics 387 11.5: Rotation of Axes 391 11.6: Polar Equations of Conics 397 Chapter 11 Review 402 Chapter 11 Test 407 Focus on Modeling: Conics in Architecture 408 Cumulative Review Test: Chapters 10 and 11 409 Ch 12: Sequences and Series 411 12.1: Sequences and Summation Notation 411 12.2: Arithmetic Sequences 413 12.3: Geometric Sequences 415 12.4: Mathematics of Finance 419 12.5: Mathematical Induction 421 12.6: The Binomial Theorem 426 Chapter 12 Review 428 Chapter 12 Test 432 Focus on Modeling: Modeling with Recursive Sequences 432 Ch 13: Limits: A Preview of Calculus 435 13.1: Finding Limits Numerically and Graphically 435 13.2: Finding Limits Algebraically 437 13.3: Tangent Lines and Derivatives 440 13.4: Limits at Infinity; Limits of Sequences 442 13.5: Areas 444 Chapter 13 Review 447 Chapter 13 Test 450 Focus on Modeling: Interpretations of Area 452 Cumulative Review Test: Chapters 12 and 13 454