INSTRUCTOR’S SOLUTIONS MANUAL — Calculus & Its Applications, Brief Version, 15th Edition — Larry J. Goldstein; David C. Lay; David I. Schneider; Nakhle H. Asmar; William Edward Tavernetti — ISBN 9780137638598

INSTRUCTOR’S
SOLUTIONS MANUAL

CALCULUS AND ITS A PPLICATIONS
FIFTEENTH EDITION

CALCULUS AND ITS APPLICATIONS ,
BRIEF V ERSION
FIFTEENTH EDITION

Larry J. Goldstein
Goldstein Educational Technologies


David C. Lay
University of Maryland


David I. Schneider
University of Maryland


Nakhlé H. Asmar
University of Missouri

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ISBN-13: 978-0-13-759103-9

, CONTENTS

Chapter 0 Functions .............................................................................................1
Chapter 1 The Derivative ...................................................................................26
Chapter 2 Applications of the Derivative.......................................................... 73
Chapter 3 Techniques of Differentiation ......................................................... 121
Chapter 4 The Exponential and Natural Logarithmic Functions .....................147
Chapter 5 Applications of the Exponential and Natural Logarithm
Functions .........................................................................................177
Chapter 6 The Definite Integral .......................................................................196
Chapter 7 Functions of Several Variables....................................................... 230
Chapter 8 The Trigonometric Functions ..........................................................267
Chapter 9 Techniques of Integration ............................................................... 286
Chapter 10 Differential Equations .....................................................................327
Chapter 11 Taylor Polynomials and Infinite Series. ..........................................360
Chapter 12 Probability and Calculus ................................................................ 382

, Chapter 0 Functions
0.1 Functions and Their Graphs 16. h(s) =
s
1. (1 + s)
⎛1⎞ 1 1
2. h⎜ ⎟ = 2 = 2 = 1
⎝2⎠ ( )
1 + 21 3
2
3
3.
h⎛ ⎞
3
⎜⎝− ⎟ = – 2 = – 2 = 3
3 3
⎠
4.
2 1+ − 3
2
( )
– 12
a +1 a +1
h(a + 1) = =
5. 1 + (a + 1) a + 2

6. 17. f (x) = 3x + 2, h ≠ 0
f (3 + h) = 3(3 + h) + 2 = 9 + 3h + 2 = 3h + 11
⎛ 3⎞
7. [2, 3) 8. ⎜ −1, ⎟ f (3) = 3(3) + 2 = 11
⎝ 2⎠
f (3 + h) − f (3) (3h + 11) − 11 = 3h = 3
=
9. [–1, 0) 10. [–1, 8) h h h
11. (−∞, 3) 12. ⎡⎣ 2, ∞ ) 18. f (x) = x 2 , h ≠ 0

13. f (x) = x 2 − 3x f (1 + h) = (1 + h)2 = 1 + 2h + h2
f (1) = 12 = 1
f (0) = 0 2 − 3(0) = 0

f (5) = 52 − 3(5) = 25 − 15 = 10 ( 2
f (1 + h) − f (1) 1 + 2h + h − 1
=
)
h h
f (3) = 32 − 3(3) = 9 − 9 = 0 2h + h2
= = 2+ h
f (−7) = (−7)2 − 3(−7) = 49 + 21 = 70 h

14. f (x) = x3 + x2 − x − 1 19. a. k (x) = x + 273
5933 = x + 273 ⇒ x = 5660
f (1) = 13 + 12 − 1 − 1 = 0
The boiling point of tungsten is 5660C.
f (−1) = (−1)3 + (−1)2 − (−1) − 1 = 0 9
⎞3 + ⎜⎛ 1 ⎞⎟2 – ⎛ 1 ⎞ − 1 = − 9 b. f (x) = x + 32
f ⎜⎛ 1 ⎟
⎞=⎜
⎛1⎟ 59
⎝ 2 ⎠ ⎝ 2 ⎠ ⎝ 2 ⎠ ⎜⎝ 2 ⎠⎟
f (x) = (5660) + 32 = 10220
8
f (a) = a 3 + a 2 − a − 1 5
The boiling point of tungsten is 10220F.
15. f (x) = x 2 − 2x 20. a. f (0) represents the number of laptops sold
in 2015.
f (a + 1) = (a + 1)2 − 2(a + 1)
= (a 2 + 2a + 1) − 2a − 2 = a 2 − 1 b. f (5) = 150 + 2(5) + 52
f (a + 2) = (a + 2)2 − 2(a + 2) = 150 + 10 + 25 = 185
In 2020, the company will sell 185
= (a 2 + 4a + 4) − 2a − 4 = a 2 + 2a laptops.
8x
21. f (x) =
(x − 1)(x − 2)
all real numbers such that x ≠ 1, 2 or
(−∞, −1) (−1, 2) (2, ∞)



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