Barron's AP Calculus

by Brock, David; Hockett, Shirley O.

• ISBN13: 9781438071275
• ISBN10: 1438071272
• Edition: 11th
• Format: Paperback
• Copyright: 2012-02-01
• Publisher: Barrons Test Prep

Summary

Both Calculus AB and Calculus BC are covered in this comprehensive AP test preparation manual. Main features include: Four practice exams in Calculus AB and four more in Calculus BC All test questions answered with solutions explained A detailed subject review covering topics for both exams Advice to students on efficient use of their graphing calculators An enclosed CD-ROM presents two more practice tests with answers, one in Calculus AB, and the other in Calculus BC

Table of Contents

Barron's Essential 5	p. vii
Introduction	p. 1
The Courses	p. 1
Topics That May Be Tested on the Calculus AB Exam	p. 1
Topics That May Be Tested on the Calculus BC Exam	p. 2
The Examinations	p. 3
The Graphing Calculator: Using Your Graphing Calculator on the AP Exam	p. 4
Grading the Examinations	p. 9
The CLEP Calculus Examination	p. 10
This Review Book	p. 10
Flash Cards	p. 11
Diagnostic Tests
Calculus AB	p. 17
Calculus BC	p. 43
Topical Review and Practice
Functions	p. 67
Definitions	p. 67
Special Functions	p. 70
Polynomial and Other Rational Functions	p. 73
Trigonometric Functions	p. 73
Exponential and Logarithmic Functions	p. 76
Parametrically Defined Functions	p. 77
Practice Exercises	p. 80
Limits and Continuity	p. 87
Definitions and Examples	p. 87
Asymptotes	p. 92
Theorems on Limits	p. 93
Limit of a Quotient of Polynomials	p. 95
Other Basic Limits	p. 96
Continuity	p. 97
Practice Exercises	p. 102
Differentiation	p. 111
Definition of Derivative	p. 111
Formulas	p. 113
The Chain Rule; the Derivative of a Composite Function	p. 114
Differentiability and Continuity	p. 118
Estimating a Derivative	p. 119
Numerically	p. 119
Graphically	p. 122
Derivatives of Parametrically Defined Functions	p. 123
Implicit Differentiation	p. 124
Derivative of the Inverse of a Function	p. 126
The Mean Value Theorem	p. 128
Indeterminate Forms and L'Hôpital's Rule	p. 129
Recognizing a Given Limit as a Derivative	p. 132
Practice Exercises	p. 134
Applications of Differential Calculus	p. 159
Slope; Critical Points	p. 159
Tangents and Normals	p. 161
Increasing and Decreasing Functions	p. 162
Functions with Continuous Derivatives	p. 162
Functions Whose Derivatives Have Discontinuities	p. 163
Maximum, Minimum, and Inflection Points: Definitions	p. 163
Maximum, Minimum, and Inflection Points: Curve Sketching	p. 164
Functions That Are Everywhere Differentiable	p. 164
Functions Whose Derivatives May Not Exist Everywhere	p. 168
Global Maximum or Minimum	p. 169
Differentiable Functions	p. 169
Functions That Are Not Everywhere Differentiable	p. 170
Further Aids in Sketching	p. 170
Optimization: Problems Involving Maxima and Minima	p. 172
Relating a Function and Its Derivatives Graphically	p. 176
Motion Along a Line	p. 179
Motion Along a Curve: Velocity and Acceleration Vectors	p. 181
Tangent-Line Approximations	p. 185
Related Rates	p. 188
Slope of a Polar Curve	p. 190
Practice Exercises	p. 192
Antidifferentiation	p. 215
Antiderivatives	p. 215
Basic Formulas	p. 215
Integration by Partial Fractions	p. 223
Integration by Parts	p. 224
Applications of Antiderivatives; Differential Equations	p. 227
Practice Exercises	p. 229
Definite Integrals	p. 249
Fundamental Theorem of Calculus (FTC); Definition of Definite Integral	p. 249
Properties of Definite Integrals	p. 249
Integrals Involving Parametrically Defined Functions	p. 254
Definition of Definite Integral as the Limit of a Sum: The Fundamental Theorem Again	p. 255
Approximations of the Definite
Integral; Riemann Sums	p. 257
Using Rectangles	p. 257
Using Trapezoids	p. 258
Comparing Approximating Sums	p. 260
Graphing a Function from Its
Derivative; Another Look	p. 262
Interpreting In x as an Area	p. 269
Average Value	p. 270
Practice Exercises	p. 277
Applications of Integration to Geometry	p. 291
Area	p. 291
Area Between Curves	p. 293
Using Symmetry	p. 293
Volume	p. 298
Solids with Known Cross Sections	p. 298
Solids of Revolution	p. 300
Arc Length	p. 305
Improper Integrals	p. 307
Practice Exercises	p. 317
Further Applications of Integration	p. 345
Motion Along a Straight Line	p. 345
Motion Along a Plane Curve	p. 347
Other Applications of Riemann Sums	p. 350
FTC: Definite Integral of a Rate Is Net Change	p. 352
Practice Exercises	p. 356
Differential Equations	p. 367
Basic Definitions	p. 367
Slope Fields	p. 369
Euler's Method	p. 373
Solving First-Order Differential Equations Analytically	p. 377
Exponential Growth and Decay	p. 379
Exponential Growth	p. 379
Restricted Growth	p. 383
Logistic Growth	p. 386
Practice Exercises	p. 391
Sequences and Series	p. 409
Sequences of Real Numbers	p. 409
Infinite Series	p. 410
Definitions	p. 410
Theorems About Convergence or Divergence of Infinite Series	p. 412
Tests for Convergence of Infinite Series	p. 413
Tests for Convergence of Nonnegative Series	p. 414
Alternating Series and Absolute Convergence	p. 418
Power Series	p. 421
Definitions; Convergence	p. 421
Functions Defined by Power Series	p. 423
Finding a Power Series for a Function: Taylor and Maclaurin Series	p. 425
Approximating Functions with Taylor and Maclaurin Polynomials	p. 429
Taylor's Formula with Remainder; Lagrange Error Bound	p. 433
Computations with Power Series	p. 436
Power Series over Complex Numbers	p. 439
Practice Exercises	p. 440
Miscellaneous Multiple-Choice Practice Questions	p. 455
Miscellaneous Free-Response Practice Exercises	p. 491
Practice Examinations
One	p. 519
Two	p. 545
Three	p. 573
Practice Examinations
One	p. 603
Two	p. 625
Three	p. 649
Appendix: Formulas and Theorems for Reference	p. 673
Index	p. 683
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