G. Polar Functions
Practice Exercises
2 Limits and Continuity
A. Definitions and Examples
B. Asymptotes
C. Theorems on Limits
D. Limit of a Quotient of Polynomials
E. Other Basic Limits
F. Continuity
Practice Exercises
3 Differentiation
A. Definition of Derivative
B. Formulas
C. The Chain Rule; the Derivative of a Composite Function
D. Differentiability and Continuity
E. Estimating a Derivative
E1. Numerically
E2. Graphically
BC ONLY
F. Derivatives of Parametrically Defined Functions
G. Implicit Differentiation
H. Derivative of the Inverse of a Function
I. The Mean Value Theorem
J. Indeterminate Forms and L’Hôpital’s Rule
K. Recognizing a Given Limit as a Derivative
Practice Exercises
4 Applications of Differential Calculus
A. Slope; Critical Points
B. Tangents to a Curve
C. Increasing and Decreasing Functions
Case I. Functions with Continuous Derivatives
Case II. Functions Whose Derivatives Have Discontinuities