Barron's AP calculus premium
Book - 2019
Saved in:
- Subjects
- Genres
- Examination study guides
Study guides - Published
-
New York, NY :
Kaplan, Inc., d/b/a Barron's Educational Series, Inc
- Language
- English
- Item Description
- "Plus online practice."--Cover.
Access to online content may not be available. - ISBN
- 9781506291680
- ISSN
- 29938945
19403119
- How to Use This Book
- Barron's Essential 5
- Introduction
- Content Areas
- Exam Format
- Scoring of the Exams
- Using Your Graphing Calculator on the AP Exam
- Diagnostic Tests
- Diagnostic Test Calculus AB
- Answer Explanations
- Diagnostic Test Calculus BC
- Answer Explanations
- Topical Review and Practice
- 1. Functions
- A. Definitions
- B. Special Functions
- C. Polynomial and Other Rational Functions
- D. Trigonometric Functions
- E. Exponential and Logarithmic Functions
- F. Parametrically Defined Functions
- G. Polar Functions
- Practice Exercises
- Answer Explanations
- 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
- Answer Explanations
- 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
- 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'Hospital's Rule
- K. Recognizing a Given Limit as a Derivative
- Practice Exercises
- Answer Explanations
- 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
- D. Maximum, Minimum, Concavity, and Inflection Points: Definitions
- E. Maximum, Minimum, and Inflection Points: Curve Sketching
- Case I. Functions That Are Everywhere Differentiable
- Case II. Functions Whose Derivatives May Not Exist Everywhere
- F. Global Maximum or Minimum
- Case I. Differentiable Functions
- Case II. Functions That Are Not Everywhere Differentiable
- G. Further Aids in Sketching
- H. Optimization: Problems Involving Maxima and Minima
- I. Relating a Function and Its Derivatives Graphically
- J. Motion Along a Line
- K. Motion Along a Curve: Velocity and Acceleration Vectors
- L. Tangent-Line Approximations
- M. Related Rates
- N. Slope of a Polar Curve
- Practice Exercises
- Answer Explanations
- 5. Antidifferentiation
- A. Antiderivatives
- B. Basic Formulas
- C. Integration by Partial Fractions
- D. Integration by Parts
- E. Applications of Antiderivatives; Differential Equations
- Practice Exercises
- Answer Explanations
- 6. Definite Integrals
- A. Fundamental Theorem of Calculus (FTC); Evaluation of Definite integrals
- B. Properties of Definite Integrals
- C. Definition of Definite Integral as the Limit of a Riemann Sum
- D. The Fundamental Theorem Again
- E. Approximations of the Definite Integral; Riemann Sums
- E1. Using Rectangles
- E2. Using Trapezoids
- E3. Comparing Approximating Sums
- F. Graphing a Function from Its Derivative; Another Look
- G. Interpreting In x as an Area
- H. Average Value
- Practice Exercises
- Answer Explanations
- 7. Applications of Integration to Geometry
- A. Area
- A1. Area Between Curves
- A2. Using Symmetry
- A3. Region Bounded by Polar Curve
- B. Volume
- B1. Solids with Known Cross Sections
- B2. Solids of Revolution
- C. Length of Curve (Arc Length)
- D. Improper integrals
- Practice Exercises
- Answer Explanations
- 8. Further Applications of Integration
- A. Motion Along a Straight Line
- B. Motion Along a Plane Curve
- C. Other Applications of Riemann Sums
- D. FTC: Definite Integral of a Rate Is Net Change
- Practice Exercises
- Answer Explanations
- 9. Differential Equations
- A. Basic Definitions
- B. Slope Fields
- C. Euler's Method
- D. Solving First-Order Differential Equations Analytically
- E. Exponential Growth and Decay
- Case I. Exponential Growth
- Case II. Restricted Growth
- Case III. Logistic Growth
- Practice Exercises
- Answer Explanations
- 10. Sequences and Series
- A. Sequences of Real Numbers
- B. Infinite Series
- B1. Definitions
- B2. Theorems About Convergence or Divergence of Infinite Series
- B3. Tests for Convergence of Infinite Series
- B4. Tests for Convergence of Nonnegative Series
- B5. Alternating Series and Absolute Convergence
- C. Power Series
- C1. Definitions; Convergence
- C2. Functions Defined by Power Series
- C3. Finding a Power Series for a Function: Taylor and Maclaurin Series
- C4. Approximating Functions with Taylor and Maclaurin Polynomials
- C5. Taylor's Formula with Remainder; Lagrange Error Bound
- C6. Computations with Power Series
- C7. Power Series over Complex Numbers
- Practice Exercises
- Answer Explanations
- 11. Miscellaneous Multiple-Choice Practice Questions
- Answer Explanations
- 12. Miscellaneous Free-Response Practice Exercises
- Answer Explanations
- AB Practice Tests
- AB Practice Test 1
- Answer Explanations
- AB Practice Test 2
- Answer Explanations
- BC Practice Tests
- BC Practice Test 1
- Answer Explanations
- BC Practice Test 2
- Answer Explanations
- Appendix: Formulas and Theorems for Reference
- Index