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- 1.1 Introduction to Limits
- 1.2 Techniques for Finding Limits
- 1.3 A Precise Definition of a Limit
- 1.4 Continuous Functions
- 1.5 Tangent Lines and Rates of Change
- 2.01 The Derivative
- 2.02 Basic Rules of Differentiation
- 2.03 The Product and Quotient Rules
- 2.04 The Role of the Derivative in the World
- 2.05 Derivatives of Trigonometric Functions
- 2.06 The Chain Rule
- 2.07 Implicit Differentiation
- 2.09 Related Rates
- 2.10 Differentials and Linear Approximations
- 3.1 Extrema of Functions
- 3.2 The Mean Value Theorem
- 3.3 Increasing and Decreasing Functions; First Derivative Test
- 3.4 Concavity and Inflection Points
- 3.5 Limits Involving Infinity; Asymptotes
- 3.6 Curve Sketching
- 3.7 Optimization Problems
- 4.1 Indefinite Integrals
- 4.2 Integration by Substitution
- 4.3 Area
- 4.4 The Definite Integral
- 4.5 The Fundamental Theorem of Calculus
- 5.1 The Area Between Curves