Calculus: Early Transcendental Functions, 7th Edition

For The 7th Edition Of Calculus: Early Transcendental Functions, The Companion Website Larsoncalculus.com Offers Free Access To Multiple Tools And Resources To Supplement Your Learning. Stepped-out Solution Videos With Instruction Are Available At Calcview.com For Selected Exercises Throughout The Text. The Website Calcchat.com Presents Free Solutions To Odd-numbered Exercises In The Text. The Site Currently Has Over 1 Million Hits Per Month, So The Authors Analyzed These Hits To See Which Exercise Solutions You Were Accessing Most Often. They Revised And Refined The Exercise Sets Based On This Analysis. Important Notice: Media Content Referenced Within The Product Description Or The Product Text May Not Be Available In The Ebook Version. Cover......Page 1 Contents......Page 8 Preface......Page 13 Student Resources......Page 16 Instructor Resources......Page 17 Acknowledgments......Page 18 Chapter 1: Preparation for Calculus......Page 20 1.1 Graphs and Models......Page 21 1.2 Linear Models and Rates of Change......Page 29 1.3 Functions and Their Graphs......Page 38 1.4 Review of Trigonometric Functions......Page 50 1.5 Inverse Functions......Page 60 1.6 Exponential and Logarithmic Functions......Page 71 Review Exercises......Page 79 P.S. Problem Solving......Page 82 Chapter 2: Limits and Their Properties......Page 84 2.1 A Preview of Calculus......Page 85 2.2 Finding Limits Graphically and Numerically......Page 91 2.3 Evaluating Limits Analytically......Page 102 2.4 Continuity and One-Sided Limits......Page 113 2.5 Infinite Limits......Page 126 Review Exercises......Page 134 P.S. Problem Solving......Page 136 Chapter 3: Differentiation......Page 138 3.1 The Derivative and the Tangent Line Problem......Page 139 3.2 Basic Differentiation Rules and Rates of Change......Page 149 3.3 Product and Quotient Rules and Higher-Order Derivatives......Page 162 3.4 The Chain Rule......Page 173 3.5 Implicit Differentiation......Page 188 3.6 Derivatives of Inverse Functions......Page 197 3.7 Related Rates......Page 204 3.8 Newton's Method......Page 213 Review Exercises......Page 219 P.S. Problem Solving......Page 222 Chapter 4: Applications of Differentiation......Page 224 4.1 Extrema on an Interval......Page 225 4.2 Rolle's Theorem and the Mean Value Theorem......Page 233 4.3 Increasing and Decreasing Functions and the First Derivative Test......Page 240 4.4 Concavity and the Second Derivative Test......Page 250 4.5 Limits at Infinity......Page 258 4.6 A Summary of Curve Sketching......Page 268 4.7 Optimization Problems......Page 279 4.8 Differentials......Page 290 Review Exercises......Page 297 P.S. Problem Solving......Page 300 Chapter 5: Integration......Page 302 5.1 Antiderivatives and Indefinite Integration......Page 303 5.2 Area......Page 313 5.3 Riemann Sums and Definite Integrals......Page 325 5.4 The Fundamental Theorem of Calculus......Page 336 5.5 Integration by Substitution......Page 351 5.6 Indeterminate Forms and L'Hopital's Rule......Page 364 5.7 The Natural Logarithmic Function: Integration......Page 375 5.8 Inverse Trigonometric Functions: Integration......Page 384 5.9 Hyperbolic Functions......Page 392 Review Exercises......Page 402 P.S. Problem Solving......Page 404 Chapter 6: Differential Equations......Page 406 6.1 Slope Fields and Euler's Method......Page 407 6.2 Growth and Decay......Page 416 6.3 Separation of Variables......Page 424 6.4 The Logistic Equation......Page 436 6.5 First-Order Linear Differential Equations......Page 443 6.6 Predator-Prey Differential Equations......Page 450 Review Exercises......Page 457 P.S. Problem Solving......Page 460 Chapter 7: Applications of Integration......Page 462 7.1 Area of a Region between Two Curves......Page 463 7.2 Volume: The Disk Method......Page 473 7.3 Volume: The Shell Method......Page 484 7.4 Arc Length and Surfaces of Revolution......Page 493 7.5 Work......Page 504 7.6 Moments, Centers of Mass, and Centroids......Page 513 7.7 Fluid Pressure and Fluid Force......Page 524 Review Exercises......Page 530 P.S. Problem Solving......Page 532 Chapter 8: Integration Techniques and Improper Integrals......Page 534 8.1 Basic Integration Rules......Page 535 8.2 Integration by Parts......Page 542 8.3 Trigonometric Integrals......Page 551 8.4 Trigonometric Substitution......Page 560 8.5 Partial Fractions......Page 569 8.6 Numerical Integration......Page 578 8.7 Integration by Tables and Other Integration Techniques......Page 585 8.8 Improper Integrals......Page 591 Review Exercises......Page 602 P.S. Problem Solving......Page 604 Chapter 9: Infinite Series......Page 606 9.1 Sequences......Page 607 9.2 Series and Convergence......Page 618 9.3 The Integral Test and p-Series......Page 628 9.4 Comparisons of Series......Page 635 9.5 Alternating Series......Page 642 9.6 The Ratio and Root Tests......Page 650 9.7 Taylor Polynomials and Approximations......Page 659 9.8 Power Series......Page 670 9.9 Representation of Functions by Power Series......Page 680 9.10 Taylor and Maclaurin Series......Page 687 Review Exercises......Page 699 P.S. Problem Solving......Page 702 Chapter 10: Conics, Parametric Equations, and Polar Coordinates......Page 704 10.1 Conics and Calculus......Page 705 10.2 Plane Curves and Parametric Equations......Page 719 10.3 Parametric Equations and Calculus......Page 729 10.4 Polar Coordinates and Polar Graphs......Page 738 10.5 Area and Arc Length in Polar Coordinates......Page 748 10.6 Polar Equations of Conics and Kepler's Laws......Page 757 Review Exercises......Page 765 P.S. Problem Solving......Page 768 Chapter 11: Vectors and the Geometry of Space......Page 770 11.1 Vectors in the Plane......Page 771 11.2 Space Coordinates and Vectors in Space......Page 781 11.3 The Dot Product of Two Vectors......Page 789 11.4 The Cross Product of Two Vectors in Space......Page 798 11.5 Lines and Planes in Space......Page 806 11.6 Surfaces in Space......Page 817 11.7 Cylindrical and Spherical Coordinates......Page 827 Review Exercises......Page 834 P.S. Problem Solving......Page 836 Chapter 12: Vector-Valued Functions......Page 838 12.1 Vector-Valued Functions......Page 839 12.2 Differentiation and Integration of Vector-Valued Functions......Page 847 12.3 Velocity and Acceleration......Page 855 12.4 Tangent Vectors and Normal Vectors......Page 864 12.5 Arc Length and Curvature......Page 874 Review Exercises......Page 886 P.S. Problem Solving......Page 888 Chapter 13: Functions of Several Variables......Page 890 13.1 Introduction to Functions of Several Variables......Page 891 13.2 Limits and Continuity......Page 903 13.3 Partial Derivatives......Page 913 13.4 Differentials......Page 923 13.5 Chain Rules for Functions of Several Variables......Page 930 13.6 Directional Derivatives and Gradients......Page 938 13.7 Tangent Planes and Normal Lines......Page 950 13.8 Extrema of Functions of Two Variables......Page 959 13.9 Applications of Extrema......Page 967 13.10 Lagrange Multipliers......Page 975 Review Exercises......Page 983 P.S. Problem Solving......Page 986 Chapter 14: Multiple Integration......Page 988 14.1 Iterated Integrals and Area in the Plane......Page 989 14.2 Double Integrals and Volume......Page 997 14.3 Change of Variables: Polar Coordinates......Page 1009 14.4 Center of Mass and Moments of Inertia......Page 1017 14.5 Surface Area......Page 1025 14.6 Triple Integrals and Applications......Page 1032 14.7 Triple Integrals in Other Coordinates......Page 1043 14.8 Change of Variables: Jacobians......Page 1050 Review Exercises......Page 1057 P.S. Problem Solving......Page 1060 Chapter 15: Vector Analysis......Page 1062 15.1 Vector Fields......Page 1063 15.2 Line Integrals......Page 1074 15.3 Conservative Vector Fields and Independence of Path......Page 1088 15.4 Green's Theorem......Page 1098 15.5 Parametric Surfaces......Page 1107 15.6 Surface Integrals......Page 1117 15.7 Divergence Theorem......Page 1129 15.8 Stokes's Theorem......Page 1137 Review Exercises......Page 1143 P.S. Problem Solving......Page 1146 Appendix A: Proofs of Selected Theorems......Page 1149 Appedix B: Integration Tables......Page 1150 Appendix C: Precalculus Review......Page 1154 Index......Page 1286