Test Bank for Calculus Single Variable, 8th Edition, James Stewart, ISBN-10: 1305266633, ISBN-13: 9781305266636
Table of Contents
To the Student.
A Preview of Calculus.
1. FUNCTIONS AND LIMITS.
Four Ways to Represent a Function.
Mathematical Models: A Catalog of Essential Functions.
New Functions from Old Functions.
The Tangent and Velocity Problems.
The Limit of a Function.
Calculating Limits Using the Limit Laws.
The Precise Definition of a Limit.
Principles of Problem Solving.
Derivatives and Rates of Change.
Writing Project: Early Methods for Finding Tangents.
The Derivative as a Function.
Applied Project: Building a Better Roller Coaster.
Derivatives of Trigonometric Functions.
The Chain Rule.
Applied Project: Where Should a Pilot Start Descent?
Laboratory Project: Families of Implicit Curves.
Rates of Change in the Natural and Social Sciences.
Linear Approximations and Differentials.
Laboratory Project: Taylor Polynomials.
3. APPLICATION OF DIFFERENTIATION.
Maximum and Minimum Values.
Applied Project: The Calculus of Rainbows.
The Mean Value Theorem.
How Derivatives Affect the Shape of a Graph.
Limits at Infinity; Horizontal Asymptotes.
Summary of Curve Sketching.
Graphing with Calculus and Calculators.
Applied Project: The Shape of a Can.
Applied Project: Planes and Birds: Minimizing Energy.
Areas and Distances.
The Definite Integral.
Discovery Project: Area Functions.
The Fundamental Theorem of Calculus.
Indefinite Integrals and the Net Change Theorem.
Writing Project: Newton, Leibniz, and the Invention of Calculus.
The Substitution Rule.
5. APPLICATIONS OF INTEGRATION.
Areas Between Curves.
Applied Project: The Gini Index.
Volumes by Cylindrical Shells.
Average Value of a Function.
Applied Project: Calculus and Baseball.
6. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS.
Instructors may cover either Sections 6.2-6.4 or Sections 6.2*-6.4*
Exponential Functions and Their Derivatives.
Derivatives of Logarithmic Functions.
The Natural Logarithmic Function
The Natural Exponential Function.
General Logarithmic and Exponential Functions.
Exponential Growth and Decay.
Applied Project: Controlling Red Blood Cell Loss During Surgery.
Inverse Trigonometric Functions.
Applied Project: Where to Sit at the Movies.
Indeterminate Forms and l’Hospital’s Rule.
Writing Project: The Origins of l’ Hospital’s Rule
7. TECHNIQUES OF INTEGRATION.
Integration by Parts.
Integration of Rational Functions by Partial Fractions.
Strategy for Integration.
Integration Using Tables and Computer Algebra Systems.
Discovery Project: Patterns in Integrals.
8. FURTHER APPLICATIONS OF INTEGRATION.
Discovery Project: Arc Length Contest.
Area of a Surface of Revolution.
Discovery Project: Rotating on a Slant.
Applications to Physics and Engineering.
Discovery Project: Complementary Coffee Cups.
Applications to Economics and Biology.
9. DIFFERENTIAL EQUATIONS.
Modeling with Differential Equations.
Direction Fields and Euler’s Method.
Applied Project: How Fast Does a Tank Drain?
Applied Project: Which is Faster, Going Up or Coming Down?
Models for Population Growth.
10. PARAMETRIC EQUATIONS AND POLAR COORDINATES.
Curves Defined by Parametric Equations.
Laboratory Project: Running Circles Around Circles.
Calculus with Parametric Curves.
Laboratory Project: Bézier Curves.
Laboratory Project: Families of Polar Curves.
Areas and Lengths in Polar Coordinates.
Conic Sections in Polar Coordinates.
11. INFINITE SEQUENCES AND SERIES.
Laboratory Project: Logistic Sequences.
The Integral Test and Estimates of Sums.
The Comparison Tests.
Absolute Convergence and the Ratio and Root Tests.
Strategy for Testing Series.
Representations of Functions as Power Series.
Taylor and Maclaurin Series.
Laboratory Project: An Elusive Limit.
Writing Project: How Newton Discovered the Binomial Series.
Applications of Taylor Polynomials.
Applied Project: Radiation from the Stars.
A Numbers, Inequalities, and Absolute Values.
B Coordinate Geometry and Lines.
C Graphs of Second-Degree Equations.
E Sigma Notation.
F Proofs of Theorems.
G Complex Numbers.
H Answers to Odd-Numbered Exercises.