Solution Manual for Applied Calculus for the Managerial Life and Social Sciences A Brief Approach, 10th Edition, Soo T. Tan, ISBN-

Solution Manual for
Applied Calculus for the Managerial Life and Social Sciences: A Brief Approach, 10th
Edition, Soo T. Tan, ISBN-10: 1285464648, ISBN-13: 9781285464640
Chapter 1-8


Table of Contents
CHAPTER 1: PRELIMINARIES
CHAPTER 2: FUNCTIONS, LIMITS, AND THE DERIVATIVE
CHAPTER 3: DIFFERENTIATION
CHAPTER 4: APPLICATIONS OF THE DERIVATIVE
CHAPTER 5: EXPONENTIAL AND LOGARITHMIC FUNCTIONS
CHAPTER 6: INTEGRATION
CHAPTER 7: ADDITIONAL TOPICS IN INTEGRATION
CHAPTER 8: CALCULUS OF SEVERAL VARIABLES

, 1 PRELIMINARIES

1.1 Precalculus Review I

Exercises page 13

1. The interval 3 6 is shown on the number line 2. The interval 2 5] is shown on the number line
below. Note that this is an open interval indicated by below.
“” and “”. ( ] x
_2 5
( ) x
0 3 6

 
3. The interval [1 4 is shown on the number line 4. The closed interval  65   12 is shown on the
below. Note that this is a half-open interval indicated number line below.
by “[’’ (closed) and “)”(open). [ ] x
[ ) x _65 _21
_1 4


5. The infinite interval 0  is shown on the number 6. The infinite interval  5] is shown on the
line below. number line below.
( x ] x
0 5

 
 23 1 1 1
7. 2723  33  32  9. 8. 843    .
843 24 16
 0  4
9. 1  1. Recall that any number raised to the 10. 712  742  72  49.
3
zeroth power is 1.

  2  2   3  
13
1 1
  2 3
11. 8  2  22  4. 12.  13  19  93  729.

 1  12  12
75  72  1  1 1 9 16
13.  7522  7  71  7. 14. 16  9  43 .
72

 12 1 
3 6  13
15. 12523  1252312  12513  16. 2  26  2613  22  4.
12513
 15 .
   
3
32 32  3 8 8 2
17.    4  2. 18.  
3
 .
8 8 27 27 3
1

,2 1 PRELIMINARIES

 12
1658 1612 93  95 1
19.  16581278  1614  2. 20.  935212  9412  .
1678 92 81

 13 625  619
1 1
21. 1614  813  2  8 2 2  1. 22.  6251914  6251914  62
614
 36

23. True. 24. True. 32  22  3  22  62  36.

25. False. x 3  2x 2  2x 32  2x 5  2x 6 . 26. False. 33  3  27  3  30  34 .

24x 24x    2
27. False.   24x . 28. True. 22  32 2  4  92  362  62  64 .
13x 1

1 432 8 1
29. False.  43  64. 30. True.   .
43 24 16 2
 
31. False. 1212 12  1214  1. 32. True.
 23
523 2523  523 52  523 543  52  25.

1 3
33. x y2  2
. 34. 3s 13  s 73  3s 1373  3s 63  3s 2  .
x y s2

x 13 1  
35.  x 1312  x 56  56 . 36. x 1  9x 3  x 12  3x 32  3x 1232
x 12 x
3
 3x 2  .
x2
 
1 1   1 1
37. 120 s  t 3
1  . 38. x  y x 1  y 1  x  y 
s  t3 s  t3 x y
 
yx x  y x  y x 2  y2
 x  y   .
xy xy xy

x 73  12
39.  x 732  x 7363  x 133 . 40. 49x 2  4912 x 212  17 x
x 2

   1 5x 6 y 3 5x 4
41. x 2 y 3 x 5 y 3  x 25 y 33  x 3 y 0  x 3  3 . 42. 2 7
 52 x 62 y 37  52 x 4 y 4  4 .
x 2x y 2y
 2
x 34 x 3 y2 x 32 y 22 x 6 y4
43.  x 3414  x 44  x. 44.   4 .
x 14 z2 z 22 z
 23    12
x3 1 23 623 ex 1
45.  x 323 y 46.  e[xx2]12  e1  .
27y 6 27 e x2 e
 
1 2 4 9
 x 2  y  2 4.
3 x y
 2  
x 3 y 4 x 32 y 4 y 44 y8 r n 4
47.  22 4  46  10 . 48.  r 4n52n  r 4n2n5  r 6n5 .
y 2 x y x x x r 52n

, 1.1 PRECALCULUS REVIEW I 3


3
  9x 3
49. x 2  4x 5  x 23  412  x 52  x 2352  2 50. 81x 6 y 4  8112  x 62  y 42  2 .
y
 2x 116 .

   
3
51.  4 16x 4 y 8   1614  x 44  y 84  2x y 2 . 52. x 3ab  x 3ab13  x ab3 .

 
3
  13  2 12  4 12
53. 6
64x 8 y 3  6416  x 86 y 36  2x 43 y 12 . 54. 27r 6  s 2 t 4  2713 r 6 s t

 3r 2 st 2 .

   12  
55. 232  2 212  2 1414  2828. 56. 812  23  232  2 212  2828.

 34
57. 934  32  364  332  3  312 58. 612  2  312  212  312

 3 1732  5196.  1414 1732  2449.

 32
59. 1032  1012  10  3162 10  3162. 60. 100032  103  1092  104  1012

 10000 3162  31,620.

 13
61. 1025  102  1012  100 3162  3162. 62. 0000113  104  1043  10  1013

 10 2154  2154.
   
3 x 3 x 3 xy 3 xy
63.     . 64.     .
2 x x 2x xy xy xy
     
2y 3y 2y 3y 2 3y 5x 2 3x 5x 2 3x 5x 3x
65.      . 66.      .
3y 3y 3y 3 3x 3x 3x 3

3 2

3 2

3 2    
1 x x x 2x 2x y 2x y
67. 
3
 
3 2
 
3 3
 . 68.     .
x x x x y y y y
   
3 2
3
2 x x 2x x x x
69.    . 70. 
3 2
 3
.
3 x 3 x 24 x 24 x 2
     
3
2y 2y 2y 2y 3
2x 3
2x 2x2 2x
71.     . 72.  
3
    .
x x 2y 2x y 3y 3y 3
2x2 3
12x 2 y

3

3
3 3 3

3

x2z x z2 x z xz x 2 y 3 x y2 xy y
73. 
3
 
3
 
3
. 74.      .
y xz 2 y xz 2 y x z2 2x 3
xy 2 3
2x x y 2 3
2 x y2
   
75. 7x 2  2x  5  2x 2  5x  4  7x 2  2x  5  2x 2  5x  4  9x 2  3x  1.
   
76. 3x 2  5x y  2y  4  3x y  2x 2  3x 2  5x y  2y  4  3x y  2x 2  x 2  2x y  2y  4.
   
77. 5y 2  2y  1  y 2  3y  7  5y 2  2y  1  y 2  3y  7  4y 2  y  8.

78. 3 2a  b  4 b  2a  6a  3b  4b  8a  14a  7b  7 2a  b.