# Course: Cracking the AP Calculus BC Exam โข 2019 Edition

• Part I Using This Book to Improve Your AP Score
• Part II Practice Test 1
• Part III About the AP Calculus BC Exam
• Part IV Test-Taking Strategies for the AP Calculus BC Exam
• 1 How to Approach Multiple-Choice Questions
• 2 How to Approach Free-Response Questions
• Part V Content Review for the AP Calculus BC Exam
• Unit 1 Differential Calculus Essentials
• 3 Limits
• What Is a Limit?
• Limits of Trigonometric Functions
• 4 Continuity
• The Definition of Continuity
• Types of Discontinuities
• 5 The Definition of the Derivative
• Deriving the Formula
• Differentiability
• 6 Basic Differentiation
• Notation
• The Power Rule
• Higher Order Derivatives
• The Product Rule
• The Quotient Rule
• The Chain Rule
• Derivatives of Trig Functions
• Graphical Derivatives
• 7 Implicit Differentiation
• How to Do It
• Second Derivatives
• Unit 2 Differential Calculus Applications
• 8 Basic Applications of the Derivative
• Equations of Tangent Lines and Normal Lines
• The Mean Value Theorem for Derivatives
• Rolleโs Theorem
• 9 Maxima and Minima
• Applied Maxima and Minima Problems
• Curve Sketching
• 10 Motion
• Related Rates
• Position, Velocity, and Acceleration
• 11 Exponential and Logarithmic Functions, Part One
• The Derivative of ln ๐ฅ
• The Derivative of ๐^๐ฅ
• The Derivative of log_๐ (๐ฅ)
• The Derivative of ๐^๐ฅ
• 12 Other Topics in Differential Calculus
• The Derivative of an Inverse Function
• Derivatives of Parametric Functions
• LโHรดpitalโs Rule
• Differentials
• Logarithmic Differentiation
• Unit 3 Integral Calculus Essentials
• 13 The Integral
• The Antiderivative
• Integrals of Trig Functions
• ๐ข-Substitution
• 14 Definite Integrals
• Area under a Curve
• Tabular Riemann Sums
• The Mean Value Theorem for Integrals
• 15 Exponential and Logarithmic Functions, Part Two
• More Integrals of Trig Functions
• Integrating ๐^๐ฅ and ๐^๐ฅ
• 16 Integration by Parts
• The Formula
• 17 Trig Functions
• Inverse Trig Functions
• Advanced Integrals of Trig Functions
• Unit 4 Integral Calculus Applications
• 18 The Area between Two Curves
• Vertical Slices
• Horizontal Slices
• 19 The Volume of a Solid of Revolution
• Washers and Disks
• Cylindrical Shells
• Volumes of Solids with Known Cross-Sections
• 20 Other Applications of the Integral
• Length of a Curve
• Parametric Functions
• The Method of Partial Fractions
• Improper Integrals
• Calculus of Polar Curves
• 21 Differential Equations
• Separation of Variables
• Eulerโs Method
• Slope Fields
• 22 Infinite Series
• Sequences and Series
• Geometric Series
• The Ratio Test
• Comparison Test
• Limit Comparison Test
• Conditional Convergence
• Alternating Series
• Integral Test
• Error Bound
• Power Series
• Taylor Series and Polynomials

Use Nagwa in conjunction with your preferred textbook. The recommended lessons from Nagwa for each section of this textbook are provided below. This course is not affiliated with, sponsored by, or endorsed by the publisher of the referenced textbook. Nagwa is a registered trademark of Nagwa Limited. All other trademarks and registered trademarks are the property of their respective owners.