Solutions Manual for Calculus, 5th Edition – James Stewart & Stephen Kokoska (Chapters 1–13, Verified, A+ Grade)

Solution and Answer Guide: Stewart Kokoska, Calculus: Concepts and Contexts, 5e, 2024, 9780357632499, Chapter 2: Section Concept Check



SOLUTION AND ANSWER GUIDE
CALCULUS 5TH EDITION JAMES STEWART, KOKOSKA
Chapter 1-13



CHAPTER 1: SECTION 1.1

TABLE OF CONTENTS

End of Section Exercise Solutions ................................................................................................................. 1




END OF SECTION EXERCISE SOLUTIONS
1.1.1
(a) f (1) 3
(b) f ( 1) 0.2
(c) f (x) 1 when x = 0 and x = 3.
(d) f (x) 0 when x ≈ –0.8.
(e) The domain of f is 2 x 4 . The range of f is 1 y 3 .
(f) f is increasing on the interval 2 x 1 .

1.1.2
(a) f ( 4) 2; g(3) 4
(b) f (x) g(x) when x = –2 and x = 2.

(c) f (x) 1 when x ≈ –3.4.

(d) f is decreasing on the interval 0 x 4 .

(e) The domain of f is 4 x 4 . The range of f is 2 y 3 .

(f) The domain of g is 4 x 4 . The range of g is 0.5 y 4 .


1.1.3




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website, in whole or in part.

,Solution and Answer Guide: Stewart Kokoska, Calculus: Concepts and Contexts, 5e, 2024, 9780357632499, Chapter 2: Section Concept Check

(a) f (2) 12 (b) f (2) (c) f (a) 3a2 a 2
16
(d) f ( a) 3a2 a 2 (e) f (a 1) 3a2 5a (f) 2 f (x) 6a2 2a 4
(g) f (2a) 12a2 2a (h) 4
2 f (a2) 3a4 a2 2
2 2
(i) f (a) 3a2 a 2 9a4 6a3 13a2 4a 4
2
(j) f (a h) 3 a h a h 2 3a2 3h2 6ah a h 2


1.1.4

f (3 h) f (3) (4 3(3 h) (3 h)2 ) 4 9 3h 9 6h h 2) 3h h2
(3 h)
h h h h


1.1.5

f (a h) f (a) a3 3a2h 3ah2 h3 h (3a2 3ah h2)
a3 3a2 3ah h2
h h h


1.1.6

1 1 a x
f (x) f (a) a 1
x a ax ax
x
x a x a x a ax(x a) ax



1.1.7
x 3 1 3 x 3 x 3 2x x x 1
f (x) f (1) 2
x 1 1 1 x 1 2 1x x 1 1
x 1 x 1 1x x 1
x 1
x 1 1 x 1

x 1


1.1.8
x 4
The domain of f (x) is x |x 3,3 .

x2 9
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 2
website, in whole or in part.

,Solution and Answer Guide: Stewart Kokoska, Calculus: Concepts and Contexts, 5e, 2024, 9780357632499, Chapter 2: Section Concept Check

1.1.9

2x3 5 |x 3, 2 .
The domain of f (x) is x
x2 x
6




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website, in whole or in part.

, Solution and Answer Guide: Stewart Kokoska, Calculus: Concepts and Contexts, 5e, 2024, 9780357632499, Chapter 2: Section Concept Check




1.1.10

The domain of f (t)
3
2t −1 is all real numbers.



1.1.11
g t is defined when 3 t 0 t 3 and 2 t 0 t 2. Thus, the domain is t 2,
or ,
2 .

1.1.12

The domain of h(x) 1 is ,0 5, .


1.1.13

The domain of F( p) 2 − p is 0 p 4 .


1.1.14
u 1
The domain of f (u) is u |u 2, 1 .
1
1
u 1
1.1.15
(a) This function shifts the graph of y = |x| down two units and to the left one unit.
(b) This function shifts the graph of y = |x| down two units
(c) This function reflects the graph of y = |x| about the x-axis, shifts it up 3 units and then to the
left 2 units.
(d) This function reflects the graph of y = |x| about the x-axis and then shifts it up 4 units.
(e) This function reflects the graph of y = |x| about the x-axis, shifts it up 2 units then four units to
the left.
(f) This function is a parabola that opens up with vertex at (0, 5). It is not a transformation of y = |x|.


1.1.16

(a) g f x g x2 1 10 x2 1

(b) f g 4 f 10 4 402 1 1601


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website, in whole or in part.