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Appendix A Answers to Selected Exercises
1 Limits
1.1 An Introduction To Limits
1.1.3 Exercises
Terms and Concepts
1.1.3.3.
Problems
1.1.3.7.
1.1.3.9.
1.1.3.11.
1.1.3.13.
1.1.3.15.
1.1.3.17.
1.1.3.19.
1.1.3.21.
1.1.3.23.
1.1.3.25.
1.1.3.27.
1.2 Epsilon-Delta Definition of a Limit
Exercises
Terms and Concepts
1.2.3.
1.3 Finding Limits Analytically
Exercises
Problems
1.3.7.
1.3.9.
1.3.11.
1.3.13.
1.3.19.
1.3.21.
1.3.23.
1.3.25.
1.3.27.
1.3.29.
1.3.31.
1.3.33.
1.4 One-Sided Limits
Exercises
Terms and Concepts
1.4.3.
Problems
1.4.5.
1.4.5.a1.4.5.b1.4.5.c1.4.5.d1.4.5.e1.4.5.f1.4.7.
1.4.7.a1.4.7.b1.4.7.c1.4.7.d1.4.7.e1.4.7.f1.4.9.
1.4.9.a1.4.9.b1.4.9.c1.4.9.d1.4.11.
1.4.11.a1.4.11.b1.4.11.c1.4.11.d1.4.11.e1.4.11.f1.4.11.g1.4.11.h
1.4.13.
1.4.13.a1.4.13.b1.4.13.c1.4.13.d1.4.15.
1.4.15.a1.4.15.b1.4.15.c1.4.15.d1.4.15.e1.4.15.f1.4.15.g1.4.15.h1.4.17.
1.4.17.a1.4.17.b1.4.17.c1.4.17.d1.4.19.
1.4.19.a1.4.19.b1.4.19.c1.4.19.d1.4.21.
1.4.21.a1.4.21.b1.4.21.c1.4.21.d
1.5 Continuity
Exercises
Terms and Concepts
1.5.5.
1.5.7.
1.5.9.
Problems
1.5.11.
1.5.13.
1.5.15.
1.5.17.
1.5.19.
1.5.19.a1.5.19.b1.5.21.
1.5.21.a1.5.21.b
1.5.23.
1.5.25.
1.5.27.
1.5.29.
1.5.31.
1.5.33.
1.6 Limits Involving Infinity
1.6.4 Exercises
Terms and Concepts
1.6.4.1.
1.6.4.3.
1.6.4.5.
Problems
1.6.4.9.
1.6.4.9.a1.6.4.9.b1.6.4.11.
1.6.4.11.a1.6.4.11.b1.6.4.11.c1.6.4.11.d1.6.4.13.
1.6.4.13.a1.6.4.13.b
1.6.4.15.
1.6.4.15.a1.6.4.15.b1.6.4.15.c1.6.4.17.
1.6.4.17.a1.6.4.17.b1.6.4.17.c
1.6.4.19.
1.6.4.21.
1.6.4.23.
2 Derivatives
2.1 Instantaneous Rates of Change: The Derivative
2.1.3 Exercises
Terms and Concepts
2.1.3.1.
Problems
2.1.3.7.
2.1.3.9.
2.1.3.11.
2.1.3.13.
2.1.3.15.
2.1.3.17.
2.1.3.19.
2.1.3.21.
2.1.3.27.
2.1.3.27.a2.1.3.27.b2.1.3.27.c
2.2 Interpretations of the Derivative
2.2.5 Exercises
Terms and Concepts
2.2.5.1.
2.2.5.3.
Problems
2.2.5.5.
2.2.5.7.
2.2.5.9.
2.2.5.11.
2.3 Basic Differentiation Rules
2.3.3 Exercises
Terms and Concepts
2.3.3.1.
2.3.3.3.
2.3.3.5.
2.3.3.7.
2.3.3.9.
Problems
2.3.3.11.
2.3.3.13.
2.3.3.15.
2.3.3.17.
2.3.3.19.
2.3.3.21.
2.3.3.23.
2.3.3.25.
2.3.3.27.
2.3.3.29.
2.3.3.31.
2.3.3.33.
2.3.3.35.
2.3.3.37.
2.4 The Product and Quotient Rules
Exercises
Terms and Concepts
2.4.1.
2.4.3.
2.4.5.
Problems
2.4.15.
2.4.17.
2.4.19.
2.4.21.
2.4.23.
2.4.25.
2.4.27.
2.4.29.
2.4.31.
2.4.33.
2.4.35.
2.5 The Chain Rule
Exercises
Terms and Concepts
2.5.1.
2.5.3.
2.5.5.
Problems
2.5.7.
2.5.9.
2.5.11.
2.5.13.
2.5.15.
2.5.17.
2.5.19.
2.5.21.
2.5.23.
2.5.25.
2.5.27.
2.5.29.
2.5.31.
2.5.33.
2.5.35.
2.5.41.
2.6 Implicit Differentiation
2.6.4 Exercises
Terms and Concepts
2.6.4.3.
Problems
2.6.4.5.
2.6.4.7.
2.6.4.9.
2.6.4.11.
2.6.4.13.
2.6.4.15.
2.6.4.17.
2.6.4.19.
2.6.4.21.
2.6.4.23.
2.6.4.25.
2.6.4.27.
2.6.4.27.a2.6.4.27.b2.6.4.29.
2.6.4.29.a2.6.4.29.b2.6.4.31.
2.6.4.31.a2.6.4.31.b
2.6.4.37.
2.6.4.39.
2.6.4.41.
2.7 Derivatives of Inverse Functions
Exercises
Terms and Concepts
2.7.1.
Problems
2.7.15.
2.7.17.
2.7.19.
2.7.21.
2.7.23.
3 The Graphical Behavior of Functions
3.1 Extreme Values
Exercises
Terms and Concepts
3.1.5.
Problems
3.1.9.
3.1.11.
3.1.13.
3.1.15.
3.1.17.
3.1.19.
3.1.21.
3.1.23.
3.1.25.
3.2 The Mean Value Theorem
Exercises
Problems
3.2.3.
3.2.5.
3.2.7.
3.2.9.
3.2.11.
3.2.13.
3.2.15.
3.2.17.
3.2.19.
3.3 Increasing and Decreasing Functions
Exercises
Terms and Concepts
3.3.3.
3.3.5.
Problems
3.3.15.
3.3.17.
3.3.19.
3.3.21.
3.3.23.
3.4 Concavity and the Second Derivative
3.4.3 Exercises
Terms and Concepts
3.4.3.1.
3.4.3.3.
Problems
3.4.3.15.
3.4.3.17.
3.4.3.19.
3.4.3.21.
3.4.3.23.
3.4.3.25.
3.4.3.27.
3.4.3.29.
3.4.3.31.
3.4.3.33.
3.4.3.35.
3.4.3.37.
3.4.3.39.
3.4.3.41.
3.4.3.43.
3.4.3.45.
3.4.3.47.
3.4.3.49.
3.4.3.51.
3.4.3.53.
3.4.3.55.
3.5 Curve Sketching
Exercises
Terms and Concepts
3.5.3.
3.5.5.
4 Applications of the Derivative
4.1 Newton’s Method
Exercises
Terms and Concepts
4.1.1.
Problems
4.2 Related Rates
Exercises
Terms and Concepts
4.2.1.
Problems
4.2.3.
4.2.3.a4.2.3.b4.2.3.c4.2.5.
4.2.7.
4.2.7.a4.2.7.b4.2.7.c4.2.9.
4.2.9.a4.2.9.b4.2.9.c4.2.9.d4.2.11.
4.2.11.a4.2.11.b4.2.11.c4.2.11.d4.2.13.
4.2.13.a4.2.13.b4.2.13.c4.2.13.d4.2.15.
4.3 Optimization
Exercises
Terms and Concepts
4.3.1.
Problems
4.3.3.
4.3.5.
4.3.7.
4.3.9.
4.3.11.
4.3.13.
4.3.15.
4.3.17.
4.4 Differentials
Exercises
Terms and Concepts
4.4.1.
4.4.3.
Problems
4.4.7.
4.4.9.
4.4.11.
4.4.13.
4.4.15.
4.4.17.
4.4.19.
4.4.21.
4.4.23.
4.4.25.
4.4.27.
4.4.29.
4.4.31.
4.4.33.
4.4.35.
4.4.35.a4.4.35.b4.4.35.c4.4.37.
4.4.37.a4.4.37.b4.4.37.c4.4.39.
5 Integration
5.1 Antiderivatives and Indefinite Integration
Exercises
Terms and Concepts
5.1.7.
Problems
5.1.9.
5.1.11.
5.1.13.
5.1.15.
5.1.17.
5.1.19.
5.1.21.
5.1.23.
5.1.25.
5.1.27.
5.1.31.
5.1.33.
5.1.35.
5.1.37.
5.1.39.
5.2 The Definite Integral
Exercises
Terms and Concepts
5.2.3.
Problems
5.2.5.
5.2.5.a5.2.5.b5.2.5.c5.2.5.d5.2.5.e5.2.5.f5.2.7.
5.2.7.a5.2.7.b5.2.7.c5.2.7.d5.2.7.e5.2.7.f5.2.9.
5.2.9.a5.2.9.b5.2.9.c5.2.9.d
5.2.11.
5.2.11.a5.2.11.b5.2.11.c5.2.11.d5.2.13.
5.2.13.a5.2.13.b5.2.13.c5.2.13.d
5.2.15.
5.2.15.a5.2.15.b5.2.15.c5.2.17.
5.2.17.a5.2.17.b5.2.17.c5.2.17.d
5.3 Riemann Sums
5.3.4 Exercises
Terms and Concepts
5.3.4.1.
5.3.4.3.
Problems
5.3.4.5.
5.3.4.7.
5.3.4.9.
5.3.4.11.
5.3.4.17.
5.3.4.19.
5.3.4.21.
5.3.4.23.
5.3.4.35.
5.3.4.37.
5.3.4.39.
5.4 The Fundamental Theorem of Calculus
5.4.6 Exercises
Terms and Concepts
5.4.6.3.
Problems
5.4.6.5.
5.4.6.7.
5.4.6.9.
5.4.6.11.
5.4.6.13.
5.4.6.15.
5.4.6.17.
5.4.6.19.
5.4.6.21.
5.4.6.23.
5.4.6.25.
5.4.6.27.
5.4.6.35.
5.4.6.37.
5.4.6.39.
5.4.6.41.
5.4.6.43.
5.4.6.45.
5.4.6.55.
5.4.6.57.
5.4.6.59.
5.5 Numerical Integration
5.5.6 Exercises
Terms and Concepts
5.5.6.1.
Problems
5.5.6.5.
5.5.6.5.a5.5.6.5.b5.5.6.5.c5.5.6.7.
5.5.6.7.a5.5.6.7.b5.5.6.7.c5.5.6.9.
5.5.6.9.a5.5.6.9.b5.5.6.9.c5.5.6.11.
5.5.6.11.a5.5.6.11.b5.5.6.11.c
5.5.6.13.
5.5.6.13.a5.5.6.13.b5.5.6.15.
5.5.6.15.a5.5.6.15.b5.5.6.17.
5.5.6.17.a5.5.6.17.b5.5.6.19.
5.5.6.19.a5.5.6.19.b
5.5.6.21.
5.5.6.21.a5.5.6.21.b5.5.6.23.
5.5.6.23.a5.5.6.23.b
6 Techniques of Antidifferentiation
6.1 Substitution
6.1.5 Exercises
Terms and Concepts
6.1.5.1.
Problems
6.1.5.3.
6.1.5.5.
6.1.5.7.
6.1.5.9.
6.1.5.11.
6.1.5.13.
6.1.5.15.
6.1.5.17.
6.1.5.19.
6.1.5.21.
6.1.5.23.
6.1.5.25.
6.1.5.27.
6.1.5.29.
6.1.5.31.
6.1.5.37.
6.1.5.39.
6.1.5.41.
6.1.5.43.
6.1.5.45.
6.1.5.47.
6.1.5.49.
6.1.5.51.
6.1.5.53.
6.1.5.55.
6.1.5.57.
6.1.5.59.
6.1.5.61.
6.1.5.63.
6.1.5.65.
6.1.5.67.
6.1.5.69.
6.1.5.71.
6.1.5.73.
6.1.5.75.
6.1.5.77.
6.1.5.79.
6.1.5.81.
6.1.5.83.
6.1.5.85.
6.2 Integration by Parts
Exercises
Terms and Concepts
6.2.1.
Problems
6.2.5.
6.2.7.
6.2.9.
6.2.11.
6.2.13.
6.2.15.
6.2.17.
6.2.19.
6.2.21.
6.2.23.
6.2.25.
6.2.27.
6.2.29.
6.2.31.
6.2.33.
6.2.41.
6.2.43.
6.2.45.
6.2.47.
6.2.49.
6.3 Trigonometric Integrals
6.3.4 Exercises
Terms and Concepts
6.3.4.1.
6.3.4.3.
Problems
6.3.4.5.
6.3.4.7.
6.3.4.9.
6.3.4.11.
6.3.4.13.
6.3.4.15.
6.3.4.17.
6.3.4.19.
6.3.4.21.
6.3.4.23.
6.3.4.25.
6.3.4.27.
6.3.4.29.
6.3.4.31.
6.3.4.33.
6.4 Trigonometric Substitution
Exercises
Terms and Concepts
6.4.1.
6.4.3.
Problems
6.4.5.
6.4.7.
6.4.9.
6.4.11.
6.4.13.
6.4.15.
6.4.17.
6.4.19.
6.4.21.
6.4.23.
6.4.25.
6.5 Partial Fraction Decomposition
Exercises
Terms and Concepts
6.5.1.
Problems
6.5.7.
6.5.9.
6.5.11.
6.5.13.
6.5.15.
6.5.17.
6.5.19.
6.5.21.
6.5.23.
6.5.25.
6.6 Hyperbolic Functions
6.6.3 Exercises
Problems
6.6.3.11.
6.6.3.13.
6.6.3.15.
6.6.3.17.
6.6.3.19.
6.6.3.21.
6.6.3.23.
6.6.3.25.
6.6.3.27.
6.6.3.29.
6.6.3.31.
6.6.3.33.
6.6.3.35.
6.6.3.37.
6.6.3.39.
6.6.3.41.
6.6.3.43.
6.7 L’Hospital’s Rule
6.7.4 Exercises
Terms and Concepts
6.7.4.3.
Problems
6.7.4.9.
6.7.4.11.
6.7.4.13.
6.7.4.15.
6.7.4.17.
6.7.4.19.
6.7.4.21.
6.7.4.23.
6.7.4.25.
6.7.4.27.
6.7.4.29.
6.7.4.31.
6.7.4.33.
6.7.4.35.
6.7.4.37.
6.7.4.39.
6.7.4.41.
6.7.4.43.
6.7.4.45.
6.7.4.47.
6.7.4.49.
6.7.4.51.
6.7.4.53.
6.8 Improper Integration
6.8.4 Exercises
Terms and Concepts
6.8.4.5.
Problems
6.8.4.7.
6.8.4.9.
6.8.4.11.
6.8.4.13.
6.8.4.15.
6.8.4.17.
6.8.4.19.
6.8.4.21.
6.8.4.23.
6.8.4.25.
6.8.4.27.
6.8.4.29.
6.8.4.31.
6.8.4.33.
6.8.4.35.
6.8.4.37.
6.8.4.39.
6.8.4.41.
6.8.4.43.
7 Applications of Integration
7.1 Area Between Curves
Exercises
Terms and Concepts
7.1.1.
Problems
7.1.5.
7.1.7.
7.1.9.
7.1.11.
7.1.19.
7.1.31.
7.2 Volume by Cross-Sectional Area; Disk and Washer Methods
Exercises
Terms and Concepts
7.2.1.
Problems
7.2.13.
7.2.13.a
7.2.13.b
7.2.13.c
7.2.13.d
7.2.15.
7.2.15.a
7.2.15.b
7.2.15.c
7.2.17.
7.2.17.a
7.2.17.b
7.2.17.c
7.2.17.d
7.3 The Shell Method
Exercises
Terms and Concepts
7.3.1.
7.3.3.
Problems
7.3.13.
7.3.13.a
7.3.13.b
7.3.13.c
7.3.13.d
7.3.15.
7.3.15.a
7.3.15.b
7.3.15.c
7.3.15.d
7.3.17.
7.3.17.a
7.3.17.b
7.4 Arc Length and Surface Area
7.4.3 Exercises
Problems
7.4.3.3.
7.4.3.5.
7.4.3.7.
7.4.3.9.
7.4.3.11.
7.4.3.13.
7.4.3.15.
7.4.3.17.
7.4.3.19.
7.4.3.21.
7.4.3.23.
7.4.3.29.
7.4.3.31.
7.4.3.33.
7.5 Work
7.5.4 Exercises
Terms and Concepts
7.5.4.1.
7.5.4.3.
Problems
7.5.4.5.
7.5.4.5.a
7.5.4.5.b
7.5.4.7.
7.5.4.7.a
7.5.4.7.b
7.5.4.7.c
7.5.4.9.
7.5.4.9.a
7.5.4.9.b
7.5.4.9.c
7.5.4.11.
7.5.4.13.
7.5.4.15.
7.5.4.17.
7.5.4.19.
7.5.4.21.
7.5.4.21.a
7.5.4.21.b
7.5.4.21.c
7.5.4.23.
7.5.4.25.
7.5.4.27.
7.6 Fluid Forces
Exercises
Terms and Concepts
7.6.1.
Problems
7.6.3.
7.6.5.
7.6.7.
7.6.9.
7.6.11.
7.6.19.
8 Differential Equations
8.1 Graphical and Numerical Solutions to Differential Equations
8.1.4 Exercises
Terms and Concepts
8.1.4.1.
8.1.4.3.
8.1.4.5.
Problems
8.2 Separable Differential Equations
8.2.2 Exercises
Problems
8.2.2.5.
8.2.2.7.
8.2.2.9.
8.2.2.11.
8.2.2.13.
8.2.2.15.
8.2.2.17.
8.2.2.19.
8.3 First Order Linear Differential Equations
8.3.2 Exercises
Problems
8.3.2.1.
8.3.2.3.
8.3.2.5.
8.3.2.7.
8.3.2.9.
8.3.2.11.
8.3.2.13.
8.3.2.15.
8.4 Modeling with Differential Equations
8.4.3 Exercises
Problems
8.4.3.1.
8.4.3.3.
8.4.3.5.
8.4.3.7.
8.4.3.9.
8.4.3.11.
9 Sequences and Series
9.1 Sequences
Exercises
Terms and Concepts
9.1.1.
9.1.3.
Problems
9.1.17.
9.1.19.
9.1.21.
9.1.23.
9.1.25.
9.1.27.
9.2 Infinite Series
9.2.4 Exercises
Terms and Concepts
9.2.4.1.
9.2.4.5.
9.3 Integral and Comparison Tests
9.3.4 Exercises
Terms and Concepts
9.3.4.1.
Problems
9.3.4.5.
9.3.4.7.
9.3.4.9.
9.3.4.11.
9.4 Ratio and Root Tests
9.4.3 Exercises
Terms and Concepts
9.4.3.1.
9.4.3.3.
Problems
9.4.3.5.
9.4.3.7.
9.4.3.9.
9.4.3.11.
9.4.3.13.
9.4.3.15.
9.4.3.17.
9.4.3.19.
9.4.3.21.
9.4.3.23.
9.5 Alternating Series and Absolute Convergence
Exercises
Terms and Concepts
9.5.3.
9.7 Taylor Polynomials
Exercises
Terms and Concepts
9.7.3.
Problems
9.7.5.
9.7.7.
9.7.9.
9.7.11.
9.7.13.
9.7.15.
9.7.17.
9.7.19.
10 Curves in the Plane
10.1 Conic Sections
10.1.4 Exercises
Problems
10.1.4.45.
10.2 Parametric Equations
10.2.4 Exercises
Terms and Concepts
10.2.4.1.
10.2.4.3.
Problems
10.2.4.9.
10.2.4.11.
10.2.4.13.
10.2.4.15.
10.2.4.17.
10.2.4.19.
10.2.4.19.a
10.2.4.19.b
10.2.4.19.c
10.2.4.19.d
10.3 Calculus and Parametric Equations
10.3.4 Exercises
Terms and Concepts
10.3.4.1.
10.3.4.3.
Problems
10.4 Introduction to Polar Coordinates
10.4.4 Exercises
Terms and Concepts
10.4.4.1.
10.4.4.3.
Problems
10.4.4.5.
10.4.4.7.
10.4.4.9.
10.4.4.11.
10.4.4.13.
10.4.4.15.
10.4.4.17.
10.4.4.19.
10.4.4.21.
10.4.4.23.
10.4.4.25.
10.4.4.27.
10.4.4.29.
10.4.4.31.
10.4.4.33.
10.4.4.35.
10.4.4.39.
10.4.4.41.
10.4.4.43.
10.4.4.45.
10.4.4.47.
10.5 Calculus and Polar Functions
10.5.5 Exercises
Problems
10.5.5.3.
10.5.5.7.
10.5.5.9.
10.5.5.19.
10.5.5.21.
10.5.5.23.
10.5.5.25.
10.5.5.29.
10.5.5.31.
10.5.5.33.
11 Vectors
11.1 Introduction to Cartesian Coordinates in Space
11.1.7 Exercises
Problems
11.1.7.7.
11.1.7.9.
11.1.7.27.
11.1.7.29.
11.1.7.31.
11.2 An Introduction to Vectors
Exercises
Problems
11.2.7.
11.2.7.a11.2.7.b11.2.9.
11.2.9.a11.2.9.b
11.2.11.
11.2.11.a
11.2.11.c
11.2.27.
11.3 The Dot Product
11.3.2 Exercises
Terms and Concepts
11.3.2.1.
Problems
11.3.2.5.
11.3.2.7.
11.3.2.9.
11.3.2.11.
11.3.2.21.
11.3.2.23.
11.3.2.25.
11.3.2.27.
11.3.2.29.
11.3.2.31.
11.3.2.33.
11.3.2.35.
11.3.2.37.
11.3.2.39.
11.4 The Cross Product
11.4.3 Exercises
Terms and Concepts
11.4.3.1.
11.4.3.3.
11.4.3.5.
Problems
11.4.3.7.
11.4.3.9.
11.4.3.11.
11.4.3.13.
11.4.3.15.
11.4.3.17.
11.4.3.39.
11.4.3.41.
11.5 Lines
11.5.4 Exercises
Terms and Concepts
11.5.4.1.
11.5.4.3.
Problems
11.6 Planes
11.6.2 Exercises
Terms and Concepts
11.6.2.1.
Problems
12 Vector Valued Functions
12.1 Vector-Valued Functions
12.1.4 Exercises
Terms and Concepts
12.1.4.1.
12.1.4.3.
Problems
12.1.4.21.
12.1.4.25.
12.1.4.27.
12.1.4.29.
12.2 Calculus and Vector-Valued Functions
12.2.5 Exercises
Terms and Concepts
12.2.5.1.
Problems
12.2.5.11.
12.2.5.13.
12.2.5.15.
12.3 The Calculus of Motion
12.3.3 Exercises
Problems
12.3.3.39.
12.3.3.39.a12.3.3.39.b
12.4 Unit Tangent and Normal Vectors
12.4.4 Exercises
Terms and Concepts
12.4.4.1.
12.4.4.3.
Problems
12.5 The Arc Length Parameter and Curvature
12.5.4 Exercises
Terms and Concepts
12.5.4.1.
12.5.4.3.
12.5.4.5.
Problems
13 Functions of Several Variables
13.2 Limits and Continuity of Multivariable Functions
13.2.5 Exercises
Problems
13.3 Partial Derivatives
13.3.7 Exercises
Terms and Concepts
13.3.7.3.
Problems
13.5 The Multivariable Chain Rule
13.5.3 Exercises
Terms and Concepts
13.5.3.5.
Problems
13.5.3.7.
13.5.3.9.
13.5.3.11.
13.6 Directional Derivatives
13.6.3 Exercises
Terms and Concepts
13.6.3.3.
Problems
13.6.3.13.
13.6.3.13.a
13.6.3.13.b
13.6.3.15.
13.6.3.15.a
13.6.3.15.b
13.6.3.17.
13.6.3.17.a
13.6.3.17.b
13.6.3.19.
13.6.3.19.a
13.6.3.19.b
13.6.3.19.c
13.6.3.19.d
13.6.3.21.
13.6.3.21.a
13.6.3.21.b
13.6.3.21.c
13.6.3.21.d
13.6.3.23.
13.6.3.23.a
13.6.3.23.b
13.6.3.23.c
13.6.3.23.d
13.6.3.25.
13.6.3.25.a
13.6.3.25.b
13.6.3.27.
13.6.3.27.a
13.6.3.27.b
13.7 Tangent Lines, Normal Lines, and Tangent Planes
13.7.5 Exercises
Terms and Concepts
13.7.5.3.
13.8 Extreme Values
13.8.3 Exercises
Terms and Concepts
13.8.3.1.
13.8.3.3.
Problems
14 Multiple Integration
14.1 Iterated Integrals and Area
14.1.4 Exercises
Terms and Concepts
14.1.4.3.
Problems
14.1.4.5.
14.1.4.5.a
14.1.4.5.b
14.1.4.7.
14.1.4.7.a
14.1.4.7.b
14.1.4.9.
14.1.4.9.a
14.1.4.9.b
14.3 Double Integration with Polar Coordinates
Exercises
Problems
14.5 Surface Area
Exercises
Problems
14.6 Volume Between Surfaces and Triple Integration
14.6.4 Exercises
Problems
14.6.4.9.
14.6.4.11.
14.6.4.13.
14.6.4.15.
14.7 Triple Integration with Cylindrical and Spherical Coordinates
14.7.3 Exercises
Problems
15 Vector Analysis
15.1 Introduction to Line Integrals
15.1.4 Exercises
Terms and Concepts
15.1.4.1.
15.1.4.3.
Problems
15.1.4.5.
15.1.4.7.
15.1.4.9.
15.2 Vector Fields
15.2.3 Exercises
Terms and Concepts
15.2.3.1.
15.2.3.3.
Problems
15.2.3.9.
15.2.3.11.
15.2.3.13.
15.2.3.15.
15.2.3.17.
15.3 Line Integrals over Vector Fields
15.3.4 Exercises
Terms and Concepts
15.3.4.1.
15.3.4.3.
15.3.4.5.
Problems
15.3.4.7.
15.3.4.9.
15.3.4.11.
15.4 Flow, Flux, Green’s Theorem and the Divergence Theorem
15.4.4 Exercises
Terms and Concepts
15.4.4.1.
15.4.4.3.
15.4.4.5.
Problems
15.4.4.7.
15.4.4.9.
15.4.4.11.
15.5 Parametrized Surfaces and Surface Area
15.5.3 Exercises
Terms and Concepts
15.5.3.1.
Problems
15.5.3.9.
15.5.3.11.
15.5.3.13.
15.5.3.15.
15.6 Surface Integrals
15.6.3 Exercises
Terms and Concepts
15.6.3.1.
15.6.3.3.
Problems
15.6.3.7.
15.6.3.9.
15.6.3.11.
15.6.3.13.
15.7 The Divergence Theorem and Stokes’ Theorem
15.7.4 Exercises
Terms and Concepts
15.7.4.1.
15.7.4.3.
Problems
