Barrons AP Calculus

(Marvins-Underground-K-12) #1
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
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