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1 The Two Central Concepts in Calculus
1.1 The Two Central Concepts of Calculus
1.2 The Tangent Line Problem for Circles and Parabolas
1.3 The Area Problem
1.4 Review
1.5 Answers to Exercises in Chapter 1
2 Limits Continuity Derivatives
2.1 Difference Quotients of Polynomial Functions
2.2 The Tangent Line Problem
2.3 Limits Continuity Derivatives 1
2.4 Limits
2.5 Review
2.6 Answers to Exercises in Chapter 2
3 The Definite Integral
3.1 Approximation Method to Compute Area
3.2 The Summation (or Sigma) Notation
3.3 Approximating Area with \(n\) Rectangular Regions
3.4 Definite Integral
3.5 Comparison Properties of the Definite Integral
Chapter 3 Section 6
Chapter 3 Section 7
Chapter 3 Section 8
Chapter 3, Answers
4 Derivatives
4.1 Prior Knowledge from Trigonometry
4.2 Limits and Continuity of Trigonometric Functions
4.3 Derivatives of Trigonometric Functions
4.4 Variations on Derivatives of Trigonometric Functions
4.5 The Chain Rule and Implicit Differentiation
4.6 Related Rates
Chapter 4, Section 7
4.8 Exponential and Logarithmic Functions
Chapter 4, Answers
5 The Fundamental Theorem of Calculus
5.1 Antiderivatives
5.2 The Fundamental Theorem of Calculus Part 1
5.3 The Fundamental Theorem of Calculus Part 2
5.4 Substitution
5.5 Basic Integration Techniques
Chapter 5, Answers
6 Volume
6.1 Disk Method
6.2 Slicing Method I
6.3 Cylindrical Shells Method
6.4 Washer Method
6.5 Slicing Method II
Chapter 6, Answers
7 Consequences of the Mean Value Theorem
7.1 Chains of Theorems
7.2 Monotonic Functions and Extreme Values
7.3 Optimization
7.4 Concavity and Second Derivative Test
7.5 Graphs I. Polynomial, Rational, & Root Functions
7.6 l’Hôpital’s Rule
7.7 Graphs II: Elementary Functions
Chapter 7, Section 8
Chapter 7, Answers
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5 The Fundamental Theorem of Calculus
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