solution manual for calculus
12th edition by ron larson
bruce h. edwards latest
update 2025/2026 a+
contents
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
,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. May 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. May 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) (1, 3)
y-intercept: (0, 3) (− 4, 2) 2 (0, 2)
matches graph (d). (− 3, 1) (− 1, 1)
x
−6 − 4 (− 2, 0) 2
2
3. y = 3 − x −2
x-intercepts : ( )(
3, 0 , − 3, 0 ) 11. y = x −6
y-intercept: (0, 3)
x 0 1 4 9 16
matches graph (a).
y −6 −5 −4 −3 −2
4. y = x3 − x
y
x-intercepts: (0, 0), (−1, 0), (1, 0)
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 (1, − 5)
2 − 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. May not be copied, scanned, or duplicated, in whole or in part.
12th edition by ron larson
bruce h. edwards latest
update 2025/2026 a+
contents
Copyright 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.
,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. May 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. May 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) (1, 3)
y-intercept: (0, 3) (− 4, 2) 2 (0, 2)
matches graph (d). (− 3, 1) (− 1, 1)
x
−6 − 4 (− 2, 0) 2
2
3. y = 3 − x −2
x-intercepts : ( )(
3, 0 , − 3, 0 ) 11. y = x −6
y-intercept: (0, 3)
x 0 1 4 9 16
matches graph (a).
y −6 −5 −4 −3 −2
4. y = x3 − x
y
x-intercepts: (0, 0), (−1, 0), (1, 0)
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 (1, − 5)
2 − 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. May not be copied, scanned, or duplicated, in whole or in part.
