Solution Manual for Calculus: Single and Multivariable, 6th Edition Hughes-Hallett

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Solution Manual for Calculus: Single and Multivariable, 6th Edition, Deborah Hughes-Hallett, William G. McCallum, Andrew M. Gleason, Daniel E. Flath, Patti Frazer Lock, Sheldon P. Gordon, David O. Lomen, David Lovelock, Brad G. Osgood, Andrew Pasquale, Douglas Quinney, Jeff Tecosky-Feldman, Joseph Thrash, Karen R. Rhea, Thomas W. Tucker,,

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Table of Contents

1 A LIBRARY OF FUNCTIONS

1.1 FUNCTIONS AND CHANGE

1.2 EXPONENTIAL FUNCTIONS

1.3 NEW FUNCTIONS FROM OLD

1.4 LOGARITHMIC FUNCTIONS

1.5 TRIGONOMETRIC FUNCTIONS

1.6 POWERS, POLYNOMIALS, AND RATIONAL FUNCTIONS

1.7 INTRODUCTION TO CONTINUITY

1.8 LIMITS

REVIEW PROBLEMS

PROJECTS

2 KEY CONCEPT: THE DERIVATIVE

2.1 HOW DO WE MEASURE SPEED?

2.2 THE DERIVATIVE AT A POINT

2.3 THE DERIVATIVE FUNCTION

2.4 INTERPRETATIONS OF THE DERIVATIVE

2.5 THE SECOND DERIVATIVE

2.6 DIFFERENTIABILITY

REVIEW PROBLEMS

PROJECTS

3 SHORT-CUTS TO DIFFERENTIATION

3.1 POWERS AND POLYNOMIALS

3.2 THE EXPONENTIAL FUNCTION

3.3 THE PRODUCT AND QUOTIENT RULES

3.4 THE CHAIN RULE

3.5 THE TRIGONOMETRIC FUNCTIONS

3.6 THE CHAIN RULE AND INVERSE FUNCTIONS

3.7 IMPLICIT FUNCTIONS

3.8 HYPERBOLIC FUNCTIONS

3.9 LINEAR APPROXIMATION AND THE DERIVATIVE

3.10 THEOREMS ABOUT DIFFERENTIABLE FUNCTIONS

REVIEW PROBLEMS

PROJECTS

4 USING THE DERIVATIVE

4.1 USING FIRST AND SECOND DERIVATIVES

4.2 OPTIMIZATION

4.3 OPTIMIZATION AND MODELING

4.4 FAMILIES OF FUNCTIONS AND MODELING

4.5 APPLICATIONS TO MARGINALITY

4.6 RATES AND RELATED RATES

4.7 LHOPITALS RULE, GROWTH, AND DOMINANCE

4.8 PARAMETRIC EQUATIONS

REVIEW PROBLEMS

PROJECTS

5 KEY CONCEPT: THE DEFINITE INTEGRAL

5.1 HOW DO WE MEASURE DISTANCE TRAVELED?

5.2 THE DEFINITE INTEGRAL

5.3 THE FUNDAMENTAL THEOREM AND INTERPRETATIONS

5.4 THEOREMS ABOUT DEFINITE INTEGRALS

REVIEW PROBLEMS

PROJECTS

6 CONSTRUCTING ANTIDERIVATIVES

6.1 ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY

6.2 CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY

6.3 DIFFERENTIAL EQUATIONS AND MOTION

6.4 SECOND FUNDAMENTAL THEOREM OF CALCULUS

REVIEW PROBLEMS

PROJECTS

7 INTEGRATION

7.1 INTEGRATION BY SUBSTITUTION

7.2 INTEGRATION BY PARTS

7.3 TABLES OF INTEGRALS

7.4 ALGEBRAIC IDENTITIES AND TRIGONOMETRIC SUBSTITUTIONS

7.5 NUMERICAL METHODS FOR DEFINITE INTEGRALS

7.6 IMPROPER INTEGRALS

7.7 COMPARISON OF IMPROPER INTEGRALS

REVIEW PROBLEMS

PROJECTS

8 USING THE DEFINITE INTEGRAL

8.1 AREAS AND VOLUMES

8.2 APPLICATIONS TO GEOMETRY

8.3 AREA AND ARC LENGTH IN POLAR COORDINATES

8.4 DENSITY AND CENTER OF MASS

8.5 APPLICATIONS TO PHYSICS

8.6 APPLICATIONS TO ECONOMICS

8.7 DISTRIBUTION FUNCTIONS

8.8 PROBABILITY, MEAN, AND MEDIAN

REVIEW PROBLEMS

PROJECTS

9 SEQUENCES AND SERIES

9.1 SEQUENCES

9.2 GEOMETRIC SERIES

9.3 CONVERGENCE OF SERIES

9.4 TESTS FOR CONVERGENCE

9.5 POWER SERIES AND INTERVAL OF CONVERGENCE

REVIEW PROBLEMS

PROJECTS

10 APPROXIMATING FUNCTIONS USING SERIES

10.1 TAYLOR POLYNOMIALS

10.2 TAYLOR SERIES

10.3 FINDING AND USING TAYLOR SERIES

10.4 THE ERROR IN TAYLOR POLYNOMIAL APPROXIMATIONS

10.5 FOURIER SERIES

REVIEW PROBLEMS

PROJECTS

11 DIFFERENTIAL EQUATIONS

11.1 WHAT IS A DIFFERENTIAL EQUATION?

11.2 SLOPE FIELDS

11.3 EULERS METHOD

11.4 SEPARATION OF VARIABLES

11.5 GROWTH AND DECAY

11.6 APPLICATIONS AND MODELING

11.7 THE LOGISTIC MODEL

11.8 SYSTEMS OF DIFFERENTIAL EQUATIONS

11.9 ANALYZING THE PHASE PLANE

REVIEW PROBLEMS

PROJECTS

12 FUNCTIONS OF SEVERAL VARIABLES

12.1 FUNCTIONS OF TWO VARIABLES

12.2 GRAPHS AND SURFACES

12.3 CONTOUR DIAGRAMS

12.4 LINEAR FUNCTIONS

12.5 FUNCTIONS OF THREE VARIABLES

12.6 LIMITS AND CONTINUITY

REVIEW PROBLEMS

PROJECTS

13 A FUNDAMENTAL TOOL: VECTORS

13.1 DISPLACEMENT VECTORS

13.2 VECTORS IN GENERAL

13.3 THE DOT PRODUCT

13.4 THE CROSS PRODUCT

REVIEW PROBLEMS

PROJECTS

14 DIFFERENTIATING FUNCTIONS OF SEVERAL VARIABLES

14.1 THE PARTIAL DERIVATIVE

14.2 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY

14.3 LOCAL LINEARITY AND THE DIFFERENTIAL

14.4 GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE

14.5 GRADIENTS AND DIRECTIONAL DERIVATIVES IN SPACE

14.6 THE CHAIN RULE

14.7 SECOND-ORDER PARTIAL DERIVATIVES

14.8 DIFFERENTIABILITY

REVIEW PROBLEMS

PROJECTS

15 OPTIMIZATION: LOCAL AND GLOBAL EXTREMA

15.1 CRITICAL POINTS: LOCAL EXTREMA AND SADDLE POINTS

15.2 OPTIMIZATION

15.3 CONSTRAINED OPTIMIZATION: LAGRANGE MULTIPLIERS

REVIEW PROBLEMS

PROJECTS

16 INTEGRATING FUNCTIONS OF SEVERAL VARIABLES

16.1 THE DEFINITE INTEGRAL OF A FUNCTION OF TWO VARIABLES

16.2 ITERATED INTEGRALS

16.3 TRIPLE INTEGRALS

16.4 DOUBLE INTEGRALS IN POLAR COORDINATES

16.5 INTEGRALS IN CYLINDRICAL AND SPHERICAL COORDINATES

16.6 APPLICATIONS OF INTEGRATION TO PROBABILITY

REVIEW PROBLEMS

PROJECTS

17 PARAMETERIZATION AND VECTOR FIELDS

17.1 PARAMETERIZED CURVES

17.2 MOTION, VELOCITY, AND ACCELERATION

17.3 VECTOR FIELDS

17.4 THE FLOW OF A VECTOR FIELD

REVIEW PROBLEMS

PROJECTS

18 LINE INTEGRALS

18.1 THE IDEA OF A LINE INTEGRAL

18.2 COMPUTING LINE INTEGRALS OVER PARAMETERIZED CURVES

18.3 GRADIENT FIELDS AND PATH-INDEPENDENT FIELDS

18.4 PATH-DEPENDENT VECTOR FIELDS AND GREENS THEOREM

REVIEW PROBLEMS

PROJECTS

19 FLUX INTEGRALS AND DIVERGENCE

19.1 THE IDEA OF A FLUX INTEGRAL

19.2 FLUX INTEGRALS FOR GRAPHS, CYLINDERS, AND SPHERES

19.3 THE DIVERGENCE OF A VECTOR FIELD

19.4 THE DIVERGENCE THEOREM

REVIEW PROBLEMS

PROJECTS

20 THE CURL AND STOKES THEOREM

20.1 THE CURL OF A VECTOR FIELD

20.2 STOKES THEOREM

20.3 THE THREE FUNDAMENTAL THEOREMS

REVIEW PROBLEMS

PROJECTS

21 PARAMETERS, COORDINATES, AND INTEGRALS

21.1 COORDINATES AND PARAMETERIZED SURFACES

21.2 CHANGE OF COORDINATES IN A MULTIPLE INTEGRAL

21.3 FLUX INTEGRALS OVER PARAMETERIZED SURFACES

REVIEW PROBLEMS

PROJECTS

APPENDIX

A ROOTS, ACCURACY, AND BOUNDS

B COMPLEX NUMBERS

C NEWTONS METHOD

D VECTORS IN THE PLANE

E DETERMINANTS

READY REFERENCE

ANSWERS TO ODD-NUMBERED PROBLEMS

INDEX