Topics include: Limits and Continuity; Derivatives, Applications of Derivatives. Practice, review, and testing included. An answer key is included in this 160-page book.

The Calculus AB skills presented in this unit are those necessary in high school Advanced Placement.

Calculus AB has been divided into two volumes.

The overall format of this unit provides explanations of specific topics, followed by examples modeling the topics and exercises to reinforce proficiency of the presented topics. It is assumed that the reader is familiar with algebra, trigonometry, and pre-calculus skills.

Calculus AB includes the elements of differential and integral calculus of functions of a single variable, including standard applications such as optimization, related rates, volumes of solids of rotation, and separable differential equations. The rigorous theoretical foundations of calculus, such as delta-epsilon definition of limit, are not covered. Those more rigorous topics are left to Calculus BC.

Table of Contents

LIMITS & CONTINUITY

• Review of Function Properties
• The Meaning of Limits
• One-Sided Limits
• Nonexistent Limits
• Continuity
• Continuity & Limits of Rational Functions
• Consequences of Continuity

DERIVATIVES

• Slopes & Tangent Lines
• Definition of a Derivative
• Basic Differentiation Formulas
• Product & Quotient Rules
• Second, Third, & nth Derivatives
• Introductory Interpretation of Derivatives
• Trigonometric Limits & Derivatives
• The Chain Rule
• Derivatives of Logarithmic & Exponential Functions
• Logarithmic Differentiation
• Summary of Differentiation
• Implicit Differentiation
• Differentiating Inverse Functions

APPLICATION OF DERIVATIVES

• Differentiability & Continuity
• L'Hopital's Rule
• Maxima & Minima
• Curve Sketching
• Differentials & Linear Approximations
• Newton's Method
• Optimization Problems - Part 1
• Optimization Problems - Part 2
• Velocity & Acceleration
• Logarithmic Differentiation
• Summary of Differentiation
• Related Rates
• Mean Value Theorem

ANSWER KEY