Solutions Manual – Thomas' Calculus, 14th Edition – Joel Hass, Christopher Heil, & Maurice Weir – ISBN 9780134438986 (Full Chapters 1–16 Covered)

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Thomas' Calculus
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14th Edition
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SOLUTIONS
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MANUAL
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Joel Hass, Christopher Heil, Maurice Weir
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Comprehensive Solutions Manual for Instructors
and Students
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9780134438986
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© Joel Hass, Christopher Heil & Maurice Weir. All rights reserved.
Reproduction or distribution without permission is prohibited.




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TABLE OF CONTENTS

Solutions Manual – Thomas' Calculus (14th Edition)
Authors: Joel Hass, Christopher Heil, and Maurice Weir
ISBN: 9780134438986

PART I: FUNCTIONS, LIMITS, AND THE DERIVATIVE
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Chapter 1: Functions
Chapter 2: Limits and Continuity
Chapter 3: Derivatives
Chapter 4: Applications of Derivatives
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PART II: INTEGRATION AND DIFFERENTIAL EQUATIONS
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Chapter 5: Integrals
Chapter 6: Applications of Definite Integrals
Chapter 7: Transcendental Functions
Chapter 8: Techniques of Integration
Chapter 9: First-Order Differential Equations
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PART III: SEQUENCES, SERIES, AND CONIC SECTIONS

Chapter 10: Infinite Sequences and Series
Chapter 11: Parametric Equations and Polar Coordinates
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PART IV: MULTIVARIABLE CALCULUS

Chapter 12: Vectors and the Geometry of Space
Chapter 13: Vector-Valued Functions and Motion in Space
Chapter 14: Partial Derivatives
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Chapter 15: Multiple Integrals
Chapter 16: Integrals and Vector Fields
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CHAPTER 1 FUNCTIONS

1.1 FUNCTIONS AND THEIR GRAPHS

1. domain  (, ); range  [1, ) 2. domain  [0, ); range  (, 1]

3. domain  [2, ); y in range and y  5 x  10  0  y can be any nonnegative real number  range  [0, ).
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4. domain  (, 0]  [3, ); y in range and y  x 2  3 x  0  y can be any nonnegative real number 
range  [0, ).
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5. domain  (, 3)  (3, ); y in range and y  4 , now if t  3  3  t  0  4  0, or if t  3 
3t 3t
3  t  0  3 4 t  0  y can be any nonzero real number  range  (, 0)  (0, ).
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6. domain  (,  4)  ( 4, 4)  (4, ); y in range and y  2 , now if t  4  t 2  16  0  2  0, or if
t 2  16 t 2  16
4  t  4  16  t 2  16  0   16
2  2 2
, or if t  4  t  16  0  2  0  y can be any nonzero
t 2  16 t 2  16
real number  range  (,  18 ]  (0, ).

7. (a) Not the graph of a function of x since it fails the vertical line test.
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(b) Is the graph of a function of x since any vertical line intersects the graph at most once.

8. (a) Not the graph of a function of x since it fails the vertical line test.
(b) Not the graph of a function of x since it fails the vertical line test.
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9. base  x; (height)2   2x 
2
 x 2  height  2
3
x; area is a ( x)  1
2
(base)(height)  12 ( x)  x 
2
3
4
3 2
x ;
perimeter is p ( x)  x  x  x  3 x.

10. s  side length  s 2  s 2  d 2  s  d ; and area is a  s 2  a  12 d 2
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11. Let D  diagonal length of a face of the cube and   the length of an edge. Then  2  D 2  d 2 and

 
2 3/2 3
D 2  2 2  3 2  d 2    d . The surface area is 6 2  6d 2  2d 2 and the volume is 3  d3  d .
3 3 3 3


 
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12. The coordinates of P are x, x so the slope of the line joining P to the origin is m  xx  1 ( x  0).
x


Thus, x, x    1 , 1
.
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m2 m
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13. 2 x  4 y  5  y   12 x  54 ; L  ( x  0)2  ( y  0)2  x 2  ( 12 x  54 )2  x 2  14 x 2  54 x  16
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5 x2 5 25  20 x 2  20 x  25 20 x 2  20 x  25
 4
 4
x  16 16
 4


14. y  x  3  y 2  3  x; L  ( x  4) 2  ( y  0) 2  ( y 2  3  4)2  y 2  ( y 2  1)2  y 2
 y4  2 y2  1  y2  y4  y2  1

Copyright  2018 Pearson Education, Inc.
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2 Chapter 1 Functions
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17. The domain is (, ). 18. The domain is (, 0].
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19. The domain is (, 0)  (0, ). 20. The domain is (, 0)  (0, ).
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21. The domain is (, 5)  (5, 3]  [3, 5)  (5, ) 22. The range is [2, 3).

23. Neither graph passes the vertical line test
(a) (b)
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Copyright  2018 Pearson Education, Inc.