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Solutions C Answers to Selected Exercises

This appendix contains answers to all non-WeBWorK exercises in the text. For WeBWorK exercises, please use the HTML version of the text for access to answers and solutions.

Chapter 1 Understanding the Derivative

Section 1.1 How do we measure velocity?

Exercises 1.1.4 Exercises

Section 1.2 The notion of limit

Exercises 1.2.4 Exercises

Section 1.3 The derivative of a function at a point

Exercises 1.3.3 Exercises

Section 1.4 The derivative function

Exercises 1.4.3 Exercises

Section 1.5 Interpreting, estimating, and using the derivative

Exercises 1.5.4 Exercises

Section 1.6 The second derivative

Exercises 1.6.5 Exercises

Section 1.7 Limits, Continuity, and Differentiability

Exercises 1.7.5 Exercises

Section 1.8 The Tangent Line Approximation

Exercises 1.8.4 Exercises

Chapter 2 Computing Derivatives

Section 2.1 Elementary derivative rules

Exercises 2.1.5 Exercises

Section 2.2 The sine and cosine functions

Exercises 2.2.3 Exercises

Section 2.3 The product and quotient rules

Exercises 2.3.5 Exercises

Section 2.4 Derivatives of other trigonometric functions

Exercises 2.4.3 Exercises

Section 2.5 The chain rule

Exercises 2.5.5 Exercises

Section 2.6 Derivatives of Inverse Functions

Exercises 2.6.6 Exercises

Section 2.7 Derivatives of Functions Given Implicitly

Exercises 2.7.3 Exercises

Section 2.8 Using Derivatives to Evaluate Limits

Exercises 2.8.4 Exercises

Chapter 3 Using Derivatives

Section 3.1 Using derivatives to identify extreme values

Exercises 3.1.4 Exercises

Section 3.2 Using derivatives to describe families of functions

Exercises 3.2.3 Exercises

Section 3.3 Global Optimization

Exercises 3.3.4 Exercises

Section 3.4 Applied Optimization

Exercises 3.4.3 Exercises

Section 3.5 Related Rates

Exercises 3.5.3 Exercises

Chapter 4 The Definite Integral

Section 4.1 Determining distance traveled from velocity

Exercises 4.1.5 Exercises

Section 4.2 Riemann Sums

Exercises 4.2.5 Exercises

Section 4.3 The Definite Integral

Exercises 4.3.5 Exercises

Section 4.4 The Fundamental Theorem of Calculus

Exercises 4.4.5 Exercises

Chapter 5 Evaluating Integrals

Section 5.1 Constructing Accurate Graphs of Antiderivatives

Exercises 5.1.5 Exercises

Section 5.2 The Second Fundamental Theorem of Calculus

Exercises 5.2.5 Exercises

Section 5.3 Integration by Substitution

Exercises 5.3.5 Exercises

Section 5.4 Integration by Parts

Exercises 5.4.7 Exercises

Section 5.5 Other Options for Finding Algebraic Antiderivatives

Exercises 5.5.5 Exercises

Section 5.6 Numerical Integration

Exercises 5.6.6 Exercises

Chapter 6 Using Definite Integrals

Section 6.1 Using Definite Integrals to Find Area and Length

Exercises 6.1.5 Exercises

Section 6.2 Using Definite Integrals to Find Volume

Exercises 6.2.5 Exercises

Section 6.3 Density, Mass, and Center of Mass

Exercises 6.3.5 Exercises

Section 6.4 Physics Applications: Work, Force, and Pressure

Exercises 6.4.5 Exercises

Section 6.5 Improper Integrals

Exercises 6.5.5 Exercises

Chapter 7 Differential Equations

Section 7.1 An Introduction to Differential Equations

Exercises 7.1.5 Exercises

Section 7.2 Qualitative behavior of solutions to DEs

Exercises 7.2.4 Exercises

Section 7.3 Euler's method

Exercises 7.3.4 Exercises

Section 7.4 Separable differential equations

Exercises 7.4.3 Exercises

Section 7.5 Modeling with differential equations

Exercises 7.5.3 Exercises

Section 7.6 Population Growth and the Logistic Equation

Exercises 7.6.4 Exercises

Chapter 8 Sequences and Series

Section 8.1 Sequences

Exercises 8.1.3 Exercises

Section 8.2 Geometric Series

Exercises 8.2.3 Exercises

Section 8.3 Series of Real Numbers

Exercises 8.3.7 Exercises

Section 8.4 Alternating Series

Exercises 8.4.6 Exercises

Section 8.5 Taylor Polynomials and Taylor Series

Exercises 8.5.6 Exercises

Section 8.6 Power Series

Exercises 8.6.4 Exercises
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