Contents xvii 13 Counting and Probability 910 13.1 Counting 911 Find All the Subsets of a Set • Count the Number of Elements in a Set • Solve Counting Problems Using the Multiplication Principle 13.2 Permutations and Combinations 916 Solve Counting Problems Using Permutations Involving n Distinct Objects • Solve Counting Problems Using Combinations • Solve Counting Problems Using Permutations Involving n Nondistinct Objects 13.3 Probability 925 Construct Probability Models • Compute Probabilities of Equally Likely Outcomes • Find Probabilities of the Union of Two Events • Use the Complement Rule to Find Probabilities Chapter Review 935 Chapter Test 937 Cumulative Review 938 Chapter Project 938 14 A Preview of Calculus: The Limit, Derivative, and Integral of a Function 940 14.1 Investigating Limits Using Tables and Graphs 941 Investigate a Limit Using a Table • Investigate a Limit Using a Graph 14.2 Algebraic Techniques for Finding Limits 946 Find the Limit of a Sum, a Difference, and a Product • Find the Limit of a Polynomial • Find the Limit of a Power or a Root • Find the Limit of a Quotient • Find the Limit of an Average Rate of Change 14.3 One-sided Limits; Continuity 953 Find the One-sided Limits of a Function • Determine Whether a Function Is Continuous at a Number 14.4 The Tangent Problem; The Derivative 960 • Find an Equation of the Tangent Line to the Graph of a Function • Find the Derivative of a Function • Find Instantaneous Rates of Change • Find the Instantaneous Velocity of an Object 14.5 The Area Problem; The Integral 968 Approximate the Area under the Graph of a Function • Approximate Integrals Using a Graphing Utility Chapter Review 974 Chapter Test 977 Chapter Project 978 12.6 The Binomial Theorem 898 Evaluate ⎛ ⎝ ⎜⎜ ⎜⎜ ⎞ ⎠ ⎟⎟ ⎟⎟ n j • Use the Binomial Theorem Chapter Review 905 Chapter Test 907 Cumulative Review 908 Chapter Project 909
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