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Chapter 1: Introduction to Calculus
1.1 Radical Expressions: Rationalizing Denominators
1.2 The slope of a tangent Lesson 1 Lesson 2 Lesson 3
1.3 Rates of Change Lesson 1 Lesson 2 Lesson 3 Lesson 4
1.4 The limit of a function
1.5 Properties of Limits
1.6 Continuity
Chapter 2: Derivatives
2.1 The Derivative Function
2.2 The Derivatives of Polynomial Functions
2.3 The Product Rule
2.4 The Quotient Rule
2.5 The Derivatives of Composite Functions
Chapter 3: Derivatives and their Applications
3.1 Higher-Order Derivatives, Velocity, and Acceleration
3.2 Maximum and Minimum on an Interval
3.3 Optimization Problems
Chapter 4: Curve Sketching
4.1 Increasing and Decreasing Functions
4.2 Critical Points, Local Maxima, and Local Minima
4.3 Vertical and Horizontal Asymptotes
4.4 Concavity and Points of Inflection
Chapter 5: Derivatives of Exponential and Trigonometric Functions
5.1 Derivatives of Exponential Functions
5.2 The Derivatives of the General Exponential Functions
5.3 Optimization Problems Involving Exponential Functions
5.4 The Derivatives of Trigonometric Functions
Chapter 6
6.1 Introduction to Vectors
6.2 Vector Addition
6.3 Multiplication of a Vector by a scalar
6.4 Properties of Vectors
6.5 Vectors in R2 and R3
6.6 Operations with Algebraic Vectors in R2
6.7 Operations with Vectors in R3
6.8 Linear Combinations and Spanning Sets
Chapter 7
7.1 Vectors as Forces
7.2 Velocity
7.3 The Dot Product of Two Geometric Vectors
7.4 The Dot Product of Algebraic Vectors
7.5 Scalar and Vector Projections
7.6 The Cross Product of Two Vectors
7.7 Applications of the Dot Product and Cross Product
Chapter 8: Equations of Lines and Planes
8.1 Vectors and Parametric Equations of a Line in R2
8.2 Cartesian Equation of a line
8.3 Vector, Parametric, and Symmetric Equations of a line in R3
8.4 Vector and Parametric Equations of a Plane
8.5 The Cartesian Equation of a Plane
8.6 Sketching Planes in R3
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