Solution Manual For
Calculus & Its Applications, Brief Version
By: Larry J. Goldstein
15 Edition
, CONTENTS
Chapter 0 Functions .............................................................................................1
Chapter 1 The Derivative ...................................................................................27
Chapter 2 Applications Of The Derivative ....................................................... 74
Chapter 3 Techniques Of Differentiation ........................................................ 122
Chapter 4 The Exponential And Natural Logarithmic Functions ....................148
Chapter 5 Applications Of The Exponential And Natural Logarithm
Functions .........................................................................................178
Chapter 6 The Definite Integral .......................................................................194
Chapter 7 Functions Of Several Variables ...................................................... 227
Chapter 8 The Trigonometric Functions ..........................................................264
Chapter 9 Techniques Of Integration .............................................................. 283
Chapter 10 Differential Equations .....................................................................323
Chapter 11 Taylor Polynomials And Infinite Series. .........................................355
Chapter 12 Probability And Calculus ............................................................... 377
, Chapter 0 Functions
0.1 Functions And Their Graphs 16. H(S)
S
1. (1 + S)
1 1
=Ƒ 1
1
H = 2 = 2 =
2. 2
3. ƑH – 3
( )
1+
3
3
3
12 32
= – 2 –
= 2 =3
4.
2 1 + – 32 ( )
– 12
A +1 A +1
H(A + 1) = =
5. 1 + (A + 1) A + 2
6. 17. F (X) = 3x + 2, H S 0
F (3 + H) = 3(3 + H) + 2 = 9 + 3h + 2 = 3h + 11
Ƒ 3
7. [2, 3) 8. – F (3) = 3(3) + 2 = 11
2
1, F (3 + H) – F (3) (3h + 11) – 11 = 3h = 3
=
9. [–1, 0) 10. [–1, 8) H H H
11. (– , 3) 12. L 2, ) 18. F (X) = X 2 , H S 0
13. F (X) = X 2 – F (1 + H) = (1 + H)2 = 1 + 2h + H2
F (1) = 12 = 1
3x
F (0) = 02 – 3(0) = 0
F (5) = 52 – 3(5) = 25 – 15 =
2
F (1 + H) – F (1) 1 + 2h + H – 1
=
( )
10 H H
2h + H2
F (3) = 32 – 3(3) = 9 – 9 = 0 = = +
2 H
F (–7) = (–7) 2 – 3(–7) = 49 + 21 = H
70
14. 19. A. K (X) = X + 273
F (X) = X3 + X2 – X – 1
5933 = X + 273 → X = 5660
F (1) = 13 + 12 – 1 – 1 = 0
The Boiling Point Of Tungsten Is 5660C.
F (–1) = (–1)3 + (–1)2 – (–1) – 1 = 9
0
3 2 Ƒ1 9 B. F (X) = X + 32
FƑ 1 = Ƒ 1 + Ƒ 1 – –1 = – 59
2 2 2 2 8
F (X) = (5660) + 32 = 10220
F (A) = A3 + A 2 – A – 1 5
The Boiling Point Of Tungsten Is 10220F.
15. F (X) = X2 – 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 + Laptops.
2a
8x
21. F (X)
= (X – 1)(X –
2)
All Real Numbers Such That X ≠ 1, 2 Or
, (– , –1) V (–1, 2) V (2, )
1
Calculus & Its Applications, Brief Version
By: Larry J. Goldstein
15 Edition
, CONTENTS
Chapter 0 Functions .............................................................................................1
Chapter 1 The Derivative ...................................................................................27
Chapter 2 Applications Of The Derivative ....................................................... 74
Chapter 3 Techniques Of Differentiation ........................................................ 122
Chapter 4 The Exponential And Natural Logarithmic Functions ....................148
Chapter 5 Applications Of The Exponential And Natural Logarithm
Functions .........................................................................................178
Chapter 6 The Definite Integral .......................................................................194
Chapter 7 Functions Of Several Variables ...................................................... 227
Chapter 8 The Trigonometric Functions ..........................................................264
Chapter 9 Techniques Of Integration .............................................................. 283
Chapter 10 Differential Equations .....................................................................323
Chapter 11 Taylor Polynomials And Infinite Series. .........................................355
Chapter 12 Probability And Calculus ............................................................... 377
, Chapter 0 Functions
0.1 Functions And Their Graphs 16. H(S)
S
1. (1 + S)
1 1
=Ƒ 1
1
H = 2 = 2 =
2. 2
3. ƑH – 3
( )
1+
3
3
3
12 32
= – 2 –
= 2 =3
4.
2 1 + – 32 ( )
– 12
A +1 A +1
H(A + 1) = =
5. 1 + (A + 1) A + 2
6. 17. F (X) = 3x + 2, H S 0
F (3 + H) = 3(3 + H) + 2 = 9 + 3h + 2 = 3h + 11
Ƒ 3
7. [2, 3) 8. – F (3) = 3(3) + 2 = 11
2
1, F (3 + H) – F (3) (3h + 11) – 11 = 3h = 3
=
9. [–1, 0) 10. [–1, 8) H H H
11. (– , 3) 12. L 2, ) 18. F (X) = X 2 , H S 0
13. F (X) = X 2 – F (1 + H) = (1 + H)2 = 1 + 2h + H2
F (1) = 12 = 1
3x
F (0) = 02 – 3(0) = 0
F (5) = 52 – 3(5) = 25 – 15 =
2
F (1 + H) – F (1) 1 + 2h + H – 1
=
( )
10 H H
2h + H2
F (3) = 32 – 3(3) = 9 – 9 = 0 = = +
2 H
F (–7) = (–7) 2 – 3(–7) = 49 + 21 = H
70
14. 19. A. K (X) = X + 273
F (X) = X3 + X2 – X – 1
5933 = X + 273 → X = 5660
F (1) = 13 + 12 – 1 – 1 = 0
The Boiling Point Of Tungsten Is 5660C.
F (–1) = (–1)3 + (–1)2 – (–1) – 1 = 9
0
3 2 Ƒ1 9 B. F (X) = X + 32
FƑ 1 = Ƒ 1 + Ƒ 1 – –1 = – 59
2 2 2 2 8
F (X) = (5660) + 32 = 10220
F (A) = A3 + A 2 – A – 1 5
The Boiling Point Of Tungsten Is 10220F.
15. F (X) = X2 – 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 + Laptops.
2a
8x
21. F (X)
= (X – 1)(X –
2)
All Real Numbers Such That X ≠ 1, 2 Or
, (– , –1) V (–1, 2) V (2, )
1
