SOLUTION MANUAL FOR
CALCULUS 12TH EDITION BY
RON LARSON BRUCE H.
EDWARDS LATEST UPDATE
2025/2026 A+
Copyright 2013 Cengage Learning. All Rights Reserved. M ay not be copied, scanned, or duplicated, in whole or in part.
,contents
chapter p preparation for calculus................................................................................................1
chapter 1 limits and their properties...........................................................................................27
chapter 2 differentiation ...........................................................................................................57
chapter 3 applications of differentiation ...................................................................................110
chapter 4 integration ..............................................................................................................187
chapter 5 logarithmic, exponential, and other transcendental functions ......................................231
chapter 6 differential equations ...............................................................................................290
chapter 7 applications of integration ........................................................................................321
chapter 8 integration techniques, l’hôpital’s rule, and improper integrals ...................................371
chapter 9 infinite series...........................................................................................................449
chapter 10 conics, parametric equations, and polar coordinates ...................................................514
iii
Copyright 2013 Cengage Learning. All Rights Reserved. M ay not be copied, scanned, or duplicated, in whole or in part.
, c h a p t e r p
preparation for calculus
section p.1 graphs and models ..................................................................... 2
section p.2 linear models and rates of change ................................................ 6
section p.3 functions and their graphs......................................................... 12
section p.4 fitting models to data................................................................ 18
review exercises............................................................................................ 20
problem solving............................................................................................ 23
Copyright 2013 Cengage Learning. All Rights Reserved. M ay not be copied, scanned, or duplicated, in whole or in part.
, c h a p t e r p
preparation for calculus
section p.1 graphs and models
1. y 32 x 3 9. y x 2
x-intercept: (2, 0)
x 5 4 3 2 1 0 1
y-intercept: (0, 3)
matches graph (b). y 3 2 1 0 1 2 3
y
2. y 9 x2
6
x-intercepts: 3, 0, 3, 0
4
( 5, 3)
y-intercept: (0, 3) (1, 3)
( 4, 2) 2 (0, 2)
matches graph (d). ( 3, 1) ( 1, 1)
x
6 4 ( 2, 0) 2
3. y 3 x 2
2
x-intercepts:
3, 0 , 3, 0
11. y x 6
y-intercept: (0, 3)
matches graph (a). x 0 1 4 9 16
y 6 5 4 3 2
4. y x3 x
x-intercepts: 0, 0, 1, 0, 1, 0
y
2
y-intercept: (0, 0) x
4 4 8 12 16
matches graph (c). 2 (9, 3)
(16, 2)
4
(4, 4)
5. y 1x
2
2 (1, 5)
6
(0, 6)
8
x 4 2 0 2 4
y 0 1 2 3 4 3
13. y
y x
Copyright 2013 Cengage Learning. All Rights Reserved. M ay not be copied, scanned, or duplicated, in whole or in part.
CALCULUS 12TH EDITION BY
RON LARSON BRUCE H.
EDWARDS LATEST UPDATE
2025/2026 A+
Copyright 2013 Cengage Learning. All Rights Reserved. M ay not be copied, scanned, or duplicated, in whole or in part.
,contents
chapter p preparation for calculus................................................................................................1
chapter 1 limits and their properties...........................................................................................27
chapter 2 differentiation ...........................................................................................................57
chapter 3 applications of differentiation ...................................................................................110
chapter 4 integration ..............................................................................................................187
chapter 5 logarithmic, exponential, and other transcendental functions ......................................231
chapter 6 differential equations ...............................................................................................290
chapter 7 applications of integration ........................................................................................321
chapter 8 integration techniques, l’hôpital’s rule, and improper integrals ...................................371
chapter 9 infinite series...........................................................................................................449
chapter 10 conics, parametric equations, and polar coordinates ...................................................514
iii
Copyright 2013 Cengage Learning. All Rights Reserved. M ay not be copied, scanned, or duplicated, in whole or in part.
, c h a p t e r p
preparation for calculus
section p.1 graphs and models ..................................................................... 2
section p.2 linear models and rates of change ................................................ 6
section p.3 functions and their graphs......................................................... 12
section p.4 fitting models to data................................................................ 18
review exercises............................................................................................ 20
problem solving............................................................................................ 23
Copyright 2013 Cengage Learning. All Rights Reserved. M ay not be copied, scanned, or duplicated, in whole or in part.
, c h a p t e r p
preparation for calculus
section p.1 graphs and models
1. y 32 x 3 9. y x 2
x-intercept: (2, 0)
x 5 4 3 2 1 0 1
y-intercept: (0, 3)
matches graph (b). y 3 2 1 0 1 2 3
y
2. y 9 x2
6
x-intercepts: 3, 0, 3, 0
4
( 5, 3)
y-intercept: (0, 3) (1, 3)
( 4, 2) 2 (0, 2)
matches graph (d). ( 3, 1) ( 1, 1)
x
6 4 ( 2, 0) 2
3. y 3 x 2
2
x-intercepts:
3, 0 , 3, 0
11. y x 6
y-intercept: (0, 3)
matches graph (a). x 0 1 4 9 16
y 6 5 4 3 2
4. y x3 x
x-intercepts: 0, 0, 1, 0, 1, 0
y
2
y-intercept: (0, 0) x
4 4 8 12 16
matches graph (c). 2 (9, 3)
(16, 2)
4
(4, 4)
5. y 1x
2
2 (1, 5)
6
(0, 6)
8
x 4 2 0 2 4
y 0 1 2 3 4 3
13. y
y x
Copyright 2013 Cengage Learning. All Rights Reserved. M ay not be copied, scanned, or duplicated, in whole or in part.
