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Solution Manual For Calculus 5th Edition by James Stewart, Kokoska Chapter 1-13
Solution Manual For Calculus 5th Edition by James Stewart, Kokoska Chapter 1-13
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Solution and Answer Guide: Stewart Kokoska, Calculus: Concepts and Contexts, 5e, 2024, 9780357632499, Chapter 2: Section Concept CheckSolution 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
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 1
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) 16 (c) f (a) 3a a 2
2
(d) f (a) 3a 2 a 2 (e) f (a 1) 3a 2 5a 4 (f) 2 f ( x) 6a 2 2a 4
(g) f (2a) 12a 2 2a 2 (h) f (a 2 ) 3a 4 a 2 2
(i) f (a) 3a 2 a 2
2
9a 4 6a3 13a 2 4a 4
2
(j) f (a h) 3 a h a h 2 3a 2 3h 2 6ah a h 2
2
1.1.4
f (3 h) f (3) (4 3(3 h) (3 h) 2 ) 4 9 3h 9 6h h2 ) 3h h 2
(3 h)
h h h h
1.1.5
f (a h) f (a) a 3a h 3ah h a
3 2 2 3 3 h 3a 2 3ah h 2
3a 2 3ah h 2
h h h
1.1.6
1 1 a x
f ( x) f (a) x a ax ax ax 1
xa xa xa ax( x a) ax
1.1.7
x 3 1 3 x 3 x 3 2x 2 x 1 x 1
2
f ( x) f (1) x 1 1 1 x 1 x 1 x 1 x 1
1
x 1 x 1 x 1 x 1 x 1 x 1 x 1
1.1.8
x4
The domain of f ( x) is x | x 3,3.
x2 9
1.1.9
2 x3 5
The domain of f ( x) is x | x 3, 2.
x2 x 6
© 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
1.1.10
The domain of f (t ) 3 2t 1 is all real numbers.
1.1.11
g t 3 t 2 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
1
The domain of h( x) is ,0 5, .
4
x 5x
2
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 x 2 1 10 x 2 1
(b) f g 4 f 10 4 402 1 1601
(c) g g 1 g 10 1 10 10 100
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 3
website, in whole or in part.
, Solution and Answer Guide: Stewart Kokoska, Calculus: Concepts and Contexts, 5e, 2024, 9780357632499, Chapter 2: Section Concept Check
(d)
f g f 2 f g 22 1 f 10 5 f 50 502 1 2501
1 1 1 1
(e)
f g x f 10 x 10 x 1 100 x 2 1
2
1.1.17
The domain of h( x) 4 x is 2 x 2 , and the range is
2
0 y 2. The graph is the top half of a circle of radius 2 with center at
the origin.
1.1.18
The domain of f ( x) 1.6 x 2.4 is all real numbers.
1.1.19
t 2 1
The domain of g (t ) is t | t 1 .
t 1
1.1.20
x 1
f ( x)
The domain of x 2 1 is x | x 1,1 .
© 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 4
website, in whole or in part.
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