Calculus Graphical Numerical Algebraic 3rd Edition by Ross Finney 0132014084 978-0132014083

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ISBN-10 ‏ : ‎ 0132014084

ISBN-13 ‏ : ‎ 978-0132014083

Author: Ross L. Finney

The main goal of this third edition is to realign with the changes in the Advanced Placement (AP ) calculus syllabus and the new type of AP exam questions. We have also more carefully aligned examples and exercises and updated the data used in examples and exercises. Cumulative Quick Quizzes are now provided two or three times in each chapter.

Calculus Graphical Numerical Algebraic 3rd Table of contents:

CHAPTER 1 Prerequisites for Calculus

1.1 Lines 3
• Increments • Slope of a Line • Parallel and Perpendicular Lines • Equations of
Lines • Applications
1.2 Functions and Graphs 12
• Functions • Domains and Ranges • Viewing and Interpreting Graphs • Even
Functions and Odd Functions— Symmetry • Functions Defined in Pieces •
Absolute Value Function • Composite Functions
1.3 Exponential Functions 22
• Exponential Growth • Exponential Decay • Applications • The Number e
1.4 Parametric Equations 30
• Relations • Circles • Ellipses • Lines and Other Curves
1.5 Functions and Logarithms 37
• One-to-One Functions • Inverses • Finding Inverses • Logarithmic Functions
• Properties of Logarithms • Applications
1.6 Trigonometric Functions 46
• Radian Measure • Graphs of Trigonometric Functions • Periodicity • Even and
Odd Trigonometric Functions • Transformations of Trigonometric Graphs •
Inverse Trigonometric Functions

CHAPTER 2 Limits and Continuity 
2.1 Rates of Change and Limits 59
• Average and Instantaneous Speed • Definition of Limit • Properties of Limits
• One-sided and Two-sided Limits • Sandwich Theorem
2.2 Limits Involving Infinity 70
• Finite Limits as x —> ± °° • Sandwich Theorem Revisited • Infinite Limits as
x a • End Behavior Models • “Seeing” Limits as x —» ± 00
2.3 Continuity 78
• Continuity at a Point • Continuous Functions • Algebraic Combinations •
Composites • Intermediate Value Theorem for Continuous Functions
2.4 Rates of Change and Tangent Lines 87
• Average Rates of Change • 

CHAPTER 3 Derivatives 98
3.1 Derivative of a Function 99
• Definition of a Derivative • Notation • Relationship Between the Graphs of
f and / ‘ • Graphing the Derivative from Data • One-sided Derivatives
3.2 Differentiability 109
• How f'(a ) Might Fail to Exist • Differentiability Implies Local Linearity •
Derivatives on a Calculator • Differentiability Implies Continuity • Intermediate
Value Theorem for Derivatives
3.3 Rules for Differentiation 116
• Positive Integer Powers, Multiples, Sums, and Differences • Products and
Quotients • Negative Integer Powers of x • Second and Higher Order
Derivatives
3.4 Velocity and Other Rates of Change 127
• Instantaneous Rates of Change • Motion along a Line • Sensitivity to Change
• Derivatives in Economics
3.5 Derivatives of Trigonometric Functions 141
• Derivative of the Sine Function • Derivative of the Cosine Function • Simple
Harmonic Motion • Jerk • Derivatives of Other Basic Trigonometric Functions
3.6 Chain Rule 148
• Derivative of a Composite Function • “Outside-Inside” Rule • Repeated Use
of the Chain Rule • Slopes of Parametrized Curves • Power Chain Rule
3.7 Implicit Differentiation 157
• Implicitly Defined Functions • Lenses, Tangents, and Normal Lines •
Derivatives of Higher Order • Rational Powers of Differentiable Functions
3.8 Derivatives of Inverse Trigonometric Functions 165
• Derivatives of Inverse Functions • Derivative of the Arcsine • Derivative of the
Arctangent • Derivative of the Arcsecant • Derivatives of the Other Three
3.9 Derivatives of Exponential and Logarithmic Functions 172
• Derivative of ex • Derivative of ax • Derivative of In x • Derivative of logax •
Power Rule for Arbitrary Real Powers

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