LIMITS OF FUNCTIONS
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LIMITS OF FUNCTIONS
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Entries
59
1. Types of Function
Theory
Page 8
1A. Domain and Range of a Function
Theory
Page 8
1B. Composite Function
Theory
Page 19
1C. Inverse of a Function
Theory
Page 20
1D. Constant, Increasing and Decreasing Functions
Theory
Page 23
1E. Even and Odd Functions
Theory
Page 27
Exercises 1.1
Problem
Page 30
2. Special Functions
Theory
Page 32
2A. Piecewise Function
Theory
Page 32
2B. Absolute Value Function
Theory
Page 34
2C. Sign Function
Theory
Page 36
2D. Floor Function
Theory
Page 38
Exercises 1.2
Problem
Page 42
Chapter Summary
Theory
Page 44
Concept Check
Test
Page 44
Chapter Review Test 1A
Test
Page 45
Chapter Review Test 1B
Test
Page 47
Chapter 2. Limit of a Function
Theory
Page 50
2.1. Definition
Theory
Page 50
2.1A. Limit of a Polynomial Function
Theory
Page 50
2.1B. Limits on a Graph
Theory
Page 51
2.1C. Definition of Limit
Theory
Page 54
2.1C1. Neighborhood of a Number
Theory
Page 54
2.1C2. ε-Neighborhood of a Number
Theory
Page 55
2.1C3. Limit of a Function
Theory
Page 56
2.1D. One-Sided Limits
Theory
Page 59
2.1E. Limits of Special Functions
Theory
Page 61
2.1F. Limits Involving Infinity
Theory
Page 65
Exercises 2.1
Problem
Page 71
2.2. Indeterminate Forms
Theory
Page 75
2.2A. 0/0 as a Limit
Theory
Page 75
2.2A1. The Indeterminate Form 0/0 in Trigonometric Functions
Theory
Page 77
2.2B. ∞/∞ as a Limit
Theory
Page 81
2.2C. 0·∞ as a Limit
Theory
Page 84
2.2D. ∞−∞ as a Limit
Theory
Page 86
2.2E. 1^∞ as a Limit
Theory
Page 89
Exercises 2.2
Problem
Page 92
Chapter Summary
Theory
Page 94
Concept Check
Test
Page 94
Chapter Review Test 2A
Test
Page 95
Chapter Review Test 2B
Test
Page 97
Chapter Review Test 2C
Test
Page 99
Chapter 3. Continuity
Theory
Page 102
3.1. Continuous Functions
Theory
Page 102
3.1A. Continuity at a Point
Theory
Page 102
3.1B. Continuity on an Interval
Theory
Page 106
3.1C. Types of Discontinuity
Theory
Page 112
3.1C1. Removable Discontinuity
Theory
Page 113
3.1C2. Jump Discontinuity
Theory
Page 114
3.1C3. Infinite Discontinuity
Theory
Page 115
3.1D. Properties of a Continuous Function on a Closed Interval
Theory
Page 117
Exercises 3.1
Problem
Page 121
Chapter Summary
Theory
Page 124
Concept Check
Test
Page 124
Chapter Review Test 3A
Test
Page 125
Chapter Review Test 3B
Test
Page 127
Answers to Exercises
Answer
Page 129
Answers to Tests
Answer
Page 134
Glossary
Other
Page 135
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