CHAPTER 1, FORM A continued 38... CHAPTER 1, FORM B continued 29... CHAPTER 1, FORM C continued 23.. Does not exist... CHAPTER 1, FORM D continued 15... CHAPTER 1, FORM F continued 32.
Trang 1CHAPTER 1, FORM A
1 (a) 9, 9.7, 9.9, 9.99, 9.999, 9.9999;
11, 10.5, 10.1, 10.01, 10.001, 10.0001
(b) 10, 10, and 10
2 (a) 10
(b) 10
3 5
4 Does not exist
5 1
6 Does not exist
7 3
8 4
9 Continuous
10 Discontinuous since lim ( )
x a f x
→ does not exist for
6, 4, 2, 2, 4, 6
a= − − −
11 Does not exist
12 2
13 No
14 1
15 1
16 Yes
17 178
9
−
19 Does not exist
20 3(2− x+ h)
3
22 (0,0), 4, 32
23 17x 16
24 3 / 4 3 1/ 2
2
2
x− − x−
25 244
x
26 3 5 / 8
8x
−
27 1.28x3−14x
28 5x7−24x5+ 5
(x−4)
30 (3−x) (3 x+5) ( 72 − −x 11)
31 −8(6x−5)(6x2−10x+1)−5
32
3
3
x x
−
−
33 480x3−54
3/ 4
650
650 40
P
x
x
−
−
(b) Average cost is dropping at approximately
$2.90 per item
dr = π
6 π
(c) π in /in3
D D
37 72 / 318 3 / 4
4(2 3 ) ( 5)
x
− −
Trang 2CHAPTER 1, FORM A (continued)
38 12
39 (0.37435329, 3.0910298)
(1.8975696,−7.910868)
4
CHAPTER 1, FORM B
1 (a) 5,5.7, 5.9, 5.99, 5.999, 5.9999;
7, 6.5, 6.1, 6.01, 6.001, 6.0001
(b) 6, 6 and 6
2 (a) 6
(b) 6
3 2
4 Does not exist
5 Does not exist
6 1
7 2
8 5
9 Continuous
10 Not continuous, since
2
lim ( )
x f x
→ does not exist
11 3
12 3
13 Yes
14 Does not exist
15 2 −
16 No
17 2
18 1
9
19 Does not exist
20 10− x−5h
2
y= − x+
22 (0,0), ( 1,3)−
23 53y 52
24 5 2 / 3 1/ 2
2
25 223
x
26 2 3 / 5
5x
−
27 0.54x2−10x
28 2x2−8x+10
Trang 3CHAPTER 1, FORM B (continued)
29 (15x5 8)
x
30 (x+2) (22 −x)(2−5 )x
31 −20 (3x x2−2)(3x4−4x2+6)−6
32
2
x
−
−
33 120x
2/5
750
750 50
P
x
x
−
−
(b) Average cost is dropping by approximately
$5.22 per item
(b) 26.02 lb (c) 0.4112 lb/month
36
2
D D
3(5 4 ) (5 4 )
x
38 27
40 7 or 0.875 8
CHAPTER 1, FORM C
1 (a) 7, 7.7, 7.9, 7.99, 7.999, 7.9999
9, 8.5, 8.1, 8.01, 8.001, 8.0001
(b) 8, 8, and 8
2 (a) 8
(b) 8
3 Does not exist
4 0
5 Does not exist
6 − 3
7 1
8 6
9 Continuous
10 Not continuous since
3
lim ( ) ( 3)
x f x f
11 3−
12 1
13 No
14 4
15 4
16 Yes
17 49 −
18 7−
19 Does not exist
20 8x+4h
21 y= − + 2x 4
22 ( 1, 6), (1, 6)− −
Trang 4CHAPTER 1, FORM C (continued)
23 46x45
24 5 2 / 3 1/ 2
25 498
x
26 7 4 / 3
3x
27 18.9x2−8x
28 −2x2+32x+ 4
29 2(3x5 2)
x
30 (x+5) (44 −x)(10−7 )x
31 −3 (9x x−10)(3x3−5x2+8)−4
32
4
4
2
x x
+ +
33 360x3−24
3/5
400
400 25
P
x
x
−
−
(b) Average cost is dropping at approximately
$1,24 per item
(b) 114 ppb (c) 3 ppb/hr
( )( ) 6 (3 1) , or
D D
5(4 3 ) ( 1)
x
38 12
39 ( 0.0999004, 2.04998),
(1.0313292, 2.015982)
−
−
2
CHAPTER 1, FORM D
1 (a) 9, 8.5, 8.1, 8.01, 8.001, 8.0001;
7, 7.7, 7.9, 7.99, 7.999, 7.9999
(b) 8, 8, and− − − 8
2 (a) 8 −
(b) 8 −
3 Does not exist
4 − 1
5 2
6 0
7 Does not exist
8 4
9 Discontinuous because lim ( )
x a f x
4, 2, 2, 4
a= − − does not exist
10 Continuous
11 1−
12 1 −
13 Yes
14 Does not exist
Trang 5CHAPTER 1, FORM D (continued)
15 1
16 No
17 0
18 1
24
19 Does not exist
20 6x+3h− 7
5
22 (0,0), (1, 1) −
23 28x 27
24 1 3 / 4 1/ 2
2
25 329
x
−
26 2 5 / 7
7x
−
27 8.1x2−6x
2x + x −
29 x 312
x
−
30 (x+1) (62 −x)(16−5 )x
31 −4(6x2+32x−3)(2x3+16x2−3 )x −5
32
5
4
1
x
−
−
33 240x 3
1/ 4
550
550 45
P
x
x
−
−
(b) Average cost is dropping at approximately
$1.38 per item
dt =
(b) 770,000 people (c) 72,000 people/year
D D
8(5 2 ) ( 6)
x
−
38 75
39 (0.37260293, 1.2364915),
(1.734937, 1.511481)−
40 3 or 0.60 5
Trang 6CHAPTER 1, FORM E
10.001;
9, 9.7, 9.9, 9.99, 9.999, 9.9999
−
−
(b) 10, 10, and 10− − −
2 (a) 10 −
(b) 10 −
3 Does not exist
4 Does not exist
5 1
6 − 1
7 Does not exist
8 1
9 Not continuous, since
0
lim ( )
x f x
→ does not exist
10 Continuous
11 3 −
12 3 −
13 Yes
14 Does not exist
15 1
16 No
17 4−
18 1
18
19 Does not exist
20 10x+5h− 8
21 y= − + x 6
22 (0,0), (2, 4) −
23 113x112
24 5 2 / 3 1/ 2
3
25 6006
x
−
26 4 1/ 5
5x
−
27 2.36x3−12x
28 3x3−10x+ 4
(x−3)
30 (3−x) (2 x+1) (5 7 )2 − x
31 −8x−9(6+5x3+3x4)(6+2x3+x4)−5
32
6
6
2
x x
−
−
33 −180x2
2/3
1000
1000 25
P
x
x
−
−
(b) Average cost is dropping at approximately
$1.60 per item
(b) 24 words (c) 1.6 words/minute
2
D D
2(6 3 ) ( 10)
x
− −
38 48
CHAPTER 1, FORM E (continued)
Trang 739 (0.54368945, 3.8638885), (1, 3)
40.0
CHAPTER 1, FORM F ANSWERS
6.0001;
5, 5.7, 5.9, 5.99, 5.999, 5.9999
−
−
(b) 6,− −6, and 6−
2 (a) 6−
(b) 6−
3 0
4 Does not exist
5 − 2
6 Does not exist
7 3
8 − 2
9 Not continuous, since
2
lim ( )
x f x
→− does not exist
10 Continuous
11 Does not exist
12 2
13 No
14 5
15 5
16 Yes
17 92
18 1
40
19 Does not exist
20 8x+4h− 6
21 y= + x 8
22 (0, 0), 4, 32
3 27
−
23 85x 84
24 3 3 / 4 1/ 2
25 125
x
−
26 3 2 / 5
5x
−
27 16.4x3−10x
28 3x3+16x−161
29
2 5
4(2x 1)
x
30 2(x+2) (33 −x) (4 3 )− x
31 −16 (3x x−1)(4x3−2x2+5)−5
Trang 8CHAPTER 1, FORM F (continued)
32
4
3
x
−
−
33 480x 3
1/3
400 30,
400 30
P
x
x
−
−
(b) Average cost is dropping at
approximately $2.79 per item
(b) 99.53 F°
(c) 0.48 F/hr− °
= +
D D
6(8 2 ) (4 )
x
38 3
40 0