9780395887677

Study and Solutions Guide for Calculus

by
  • ISBN13:

    9780395887677

  • ISBN10:

    0395887674

  • Edition: 6th
  • Format: Paperback
  • Copyright: 11/12/1997
  • Publisher: Brooks Cole
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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

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