Solution Manual For Calculus & Its Applications, Brief Version, 15th edition by: Larry J. Goldstein, Complete Solutions A+

Solution Manual

Calculus & Its Applications, Brief Version,
By Larry J. Goldstein


15th 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
ƒ1 2 2 1
2. h = = =
2
3. ƒH – 3
( )
1 + 12
3
32 3
3
= – 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 – 3x f (1 + h) = (1 + h)2 = 1 + 2h + h2
F (1) = 12 = 1
F (0) = 02 – 3(0) = 0

F (5) = 52 – 3(5) = 25 – 15 = f (1 + h) – f (1)
=
1 + 2h + h2 – 1 ( )
10 h h
2h + h2
F (3) = 32 – 3(3) = 9 – 9 = 0 = = +
2 h
f (–7) = (–7) 2 – 3(–7) = 49 + 21 = 70 h

14. F (x) = x3 + x2 – x – 1 19. A. K (x) = x + 273
5933 = x + 273 → x = 5660
F (1) = 13 + 12 – 1 – 1 = 0
The boiling point of tungsten is 5660c.
F (–1) = (–1)3 + (–1)2 – (–1) – 1 = 9
0
3
FƑ 1 = ƒ 1 + ƒ 1
2 ƒ1 9 b. F (x) = x + 32
– –1 = – 59
2 2 2 2 8
3 2
f (x) =(5660) + 32 = 10220
F (a) = a + a – a – 1 5
the boiling point of tungsten is 10220f.
15. F (x) = x2 – 2x 20. A. F (0) represents the number of laptops
2 sold in 2015.
F (a + 1) = (a + 1) – 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 + 2a laptops.
8x
21. F (x)
= (x – 1)(x – 2)

, 2 Chapter 0 Functions
All real numbers such that x ≠ 1, 2 or
(– , –1) v (–1, 2) v (2, )




1 37. Positive 38. Negative
22. f (t) =
t 39. [−1, 3] 40. −1, 5, 9
all real numbers such that t > 0 or (0, ) 41. (– , – 1] v [5, 9] 42. [–1, 5] v[9, ]
1
23. g(x) = 43. f (1) .03; f (5) .037
3– x
All real numbers such that x < 3 or (– , –3) 44. f (6) .03
4 45. [0, .05] 46. T ≈ 3
24. g(x) =
X(x + 2) ƒ 1
or real numbers such that x ≠ 0, –2
All 47. f (x) = x – (x + 2)
(– , –2) v (–2, 0) v (0, ) 2
ƒ 1 25
F (3) = 3 – (3 + 2) =
25. 2 2
No, (3, 12) is not on the graph.
48. F(x) = x(5 + x)(4 – x)
F(–2) = –2(5 + (–2))(4 – (–2)) = –36
No, (–2, 12) is not on the graph.
3x – 1
26. 49. g(x) =
X2 +1
3 (1 ) – 1 2
G (1 ) = = =1
(1)2 + 1 2
Yes, (1, 1) is on the graph.
X2 + 4
50. g(x) =
X+2
27. (4 )2 + 4
20 10
g (4) = = =
ƒ 1 4 + 2 6 3
No, 4, is not on the graph.
4

51. F (x) = x3
28. F (a + 1) = (a + 1)3

ƒ5
52. f (x) = –x
x
5
F (2 + h) = – (2 + h)
(2 + h)
5 – (2 + h)2 1 – 4h – h2
= =
29. Function 30. Not a function (2 + h) 2+h

31. Not a function 32. Not a function 53. f (x) = x for 0 x < 2
33. Not a function 34. Function +
1 x for 2 x 5
35. f (0) = 1; f (7) = –1 f (1) = 1 = 1
f (2) = 1 + 2 = 3
36. f (2) = 3; f (–1) = 0 F (3) = 1 + 3 = 4