Study and Solutions Guide for Calculus

by Larson, Ron

• ISBN13: 9780395887677
• ISBN10: 0395887674
• Edition: 6th
• Format: Paperback
• Copyright: 1997-11-12
• Publisher: Brooks Cole

Table of Contents

Algebra Review	1	(222)
Preparation for Calculus
Graphs and Models	8	(2)
Linear Models and Rates of Change	10	(2)
Functions and Their Graphs	12	(2)
Fitting Models to Data	14	(3)
Review Exercises	14	(3)
Limits and Their Properties
A Preview of Calculus	17	(1)
Finding Limits Graphically and Numerically	17	(1)
Evaluating Limits Analytically	18	(2)
Continuity and One-Sided Limits	20	(3)
Infinite Limits	23	(4)
Review Exercises	25	(2)
Differentiation
The Derivative and the Tangent Line Problem	27	(2)
Basic Differentiation Rules and Rates of Change	29	(3)
The Product and Quotient Rules and Higher-Order Derivatives	32	(2)
The Chain Rule	34	(2)
Implicit Differentiation	36	(3)
Related Rates	39	(8)
Review Exercises	43	(4)
Applications of Differentiation
Extrema on an Interval	47	(32)
Rolle's Theorem and the Mean Value Theorem	79
Increasing and Decreasing Functions and the First Derivative Test	51	(34)
Concavity and the Second Derivative Test	85
Limits at Infinity	56	(2)
A Summary of Curve Sketching	58	(3)
Optimization Problems	61	(4)
Newton's Method	65	(1)
Differentials	66	(1)
Business and Economic Applications	67	(9)
Review Exercises	69	(7)
Integration
Antiderivatives and Indefinite Integration	76	(2)
Area	78	(2)
Riemann Sums and Definite Integrals	80	(743)
The Fundamental Theorem of Calculus	823
Integration by Substitution	84	(5)
Numerical Integration	89	(5)
Review Exercises	91	(3)
Logarithmic, Exponential, and Other Transcendental Functions
The Natural Logarithmic Function and Differentiation	94	(2)
The Natural Logarithmic Function and Integration	96	(2)
Inverse Functions	98	(2)
Exponential Functions: Differentiation and Integration	100	(3)
Bases Other than e and Applications	103	(1)
Differential Equations: Growth and Decay	104	(2)
Differential Equations; Separation of Variables	106	(4)
Inverse Trigonometric Functions and differentiation	110	(1)
Inverse Trigonometric Functions and Integration	111	(2)
Hyperbolic Functions	113	(5)
Review Exercises	115	(3)
Applications of Integration
Area of a Region Between Two Curves	118	(2)
Wolume: The Disc Method	120	(4)
Volume: The Shell Method	124	(3)
Arc Length and Surfaces of Revolution	127	(2)
Work	129	(2)
Moments, Centers and Mass, and Centroids	131	(3)
Fluid Pressure and Fluid Force	134	(5)
Review Exercises	134	(5)
Integration Techniques, L'Hopital's Rule, and Improper Integrals
Basic Integration Rules	139	(2)
Integration by Parts	141	(5)
Trigonometric Integrals	146	(3)
Trigonometric Substitution	149	(5)
Partial Fractions	154	(2)
Integration by Tables and Other Integration Techniques	156	(2)
Indeterminate Forms and L'Hopital's Rule	158	(2)
Improper Integrals	160	(8)
Review Exercises	163	(5)
Infinite Series
Sequences	168	(2)
Series and Convergence	170	(2)
The Integral Test and p-series	172	(1)
Comparisons of Series	173	(1)
Alternating Series	174	(2)
The Ratio and Root Tests	176	(2)
Taylor Polynomials and Approximations	178	(3)
Power Series	181	(2)
Representation of Functions by Power Series	183	(2)
Taylor and Maclaurin Series	185	(6)
Review Exercises	188	(3)
Conics, Parametric Equations, and Polar Coordinates
Conics and Calculus	191	(7)
Plane Curves and Parametric Equations	198	(3)
Parametric Equations and Calculus	201	(3)
Area and Arc Length in Polar Coordinates	204	(3)
Polar Coordinates and Polar Coordinates	207	(3)
Polar Equations of Conics and Kepler's Laws	210	(2)
Review Exercises	212	(5)
Appendices
Appendix A.1	217	(1)
Appendix A.2	218	(2)
Appendix A.3	220	(2)
Appendix E	222