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Functions, Graphs, and Models | |
Graphs and Equations | |
Functions and Models | |
Finding Domain and Range | |
Slope and Linear Functions | |
Nonlinear Functions and Models | |
Mathematical Modeling and Curve Fitting | |
Extended Technology Application: Payrolls of Professional Basketball Teams | |
Differentiation | |
Limits: A Numerical and Graphical Approach | |
Algebraic Limits and Continuity | |
Average Rates of Change | |
Differentiation Using Limits of Difference Quotients | |
Differentiation Techniques: The Power and Sum-Difference Rules | |
Differentiation Techniques: The Product and Quotient Rules | |
The Chain Rule | |
Higher-Order Derivatives | |
Extended Technology Application: Path of a Baseball: The Tale of the Tape | |
Applications of Differentiation | |
Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs | |
Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs | |
Graph Sketching: Asymptotes and Rational Functions | |
Using Derivatives to Find Absolute Maximum and Minimum Values | |
Maximum-Minimum Problems: Business and Economics Applications | |
Marginals and Differentials | |
Implicit Differentiation and Related Rates | |
Extended Technology Application: Maximum Sustainable Harvest | |
Exponential and Logarithmic Functions | |
Exponential Functions | |
Logarithmic Functions | |
Applications: The Uninhibited Growth Model, dP/dt = kP | |
Applications: Decay | |
The Derivatives of a x and logax | |
An Economics Application: Elasticity of Demand | |
Extended Technology Application: The Business of Motion Picture Box-Office Revenue | |
Integration | |
The Area Under a Graph | |
Area, Antiderivatives, and Integrals | |
Area and Definite Integrals | |
Properties of Definite Integrals | |
Integration Techniques: Substitution | |
Integration Techniques: Integration by Parts | |
Integration Techniques: Tables | |
Extended Technology Application: Financial Predictions for Starbucks, Lowes, The Gap, and Intel | |
Applications of Integration | |
An Economics Application: Consumer Surplus and Producer Surplus | |
Applications of the Models | |
Improper Integrals | |
Probability | |
Probability: Expected Value The Normal Distribution | |
Volume | |
Differential Equations | |
Extended Technology Application: Curve Fitting and the Volume of a Bottle of Soda | |
Functions of Several Variables | |
Functions of Several Variables | |
Partial Derivatives | |
Maximum-Minimum Problems | |
An Application: The Least-Squares Technique | |
Constrained Maximum and Minimum Values: Lagrange Multipliers | |
Double Integrals | |
Extended Technology Application: Minimizing Employees' Travel Time in a Building | |
Cumulative Review | |
Review of Basic Algebra | |
Tables | |
Integration Formulas | |
Areas for a Standard Normal Distribution | |
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