James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

Appendix I Answers to Odd-Numbered Exercises A103
17. y
c=3
2
c=1
22 < c < 2; 22, 0, 2
23. (a) sin 21 y − x 2 1 C
(b) y − sinsx 2 d, 2sy2 < x < sy2
1
y=sin (≈)
(c) No
_1 0 1 t
c=_1
_2
c=_3
19. (a) (i) 1.4 (ii) 1.44 (iii) 1.4641
(b) y
y=´
1.5
h=0.1
1.4
h=0.2
h=0.4
1.3
1.2
1.1
1.0
0 0.1 0.2 0.3 0.4 x
Underestimates
_œ„„„
π/2
œπ/2 „„„
0
25. cos y − cos x 2 1 5
ca070317
10.31.00
27. (a)
2.5
0
2.5
y (b) y − 1
K 2 x
3
(c) (i) 0.0918 (ii) 0.0518 (iii) 0.0277
It appears that the error is also halved (approximately).
21. 21, 23, 26.5, 212.25 23. 1.7616
25. (a) (i) 3 (ii) 2.3928 (iii) 2.3701 (iv) 2.3681
(c) (i) 20.6321 (ii) 20.0249 (iii) 20.0022 (iv) 20.0002
It appears that the error is also divided by 10 (approximately).
27. (a), (d) (b) 3
Q
(c) Yes, Q − 3
6
(e) 2.77 C
4
0 x
_3 3
_3
29. y − Cx 2 4
_4
4
2
0
2 t 4
31. x 2 2 y 2 − C
_4
4
≈-¥=C
Exercises 9.3 • page 605
1. y − 21ysx 3 1 Cd, y − 0
3. y − 6sx 2 1 2 ln | x| 1 C
5. e y 2 y − 2x 1 sin x 1 C
7. sin 1 cos − 2 1 2 e2t 2 1 C 9. p − Ke t 3 y32t
2 1
11. y − 2ln(1 2 1 2 x 2 ) 13. u − 2st 2 1 tan t 1 25
15. 1 2 y 2 1 1 3 s3 1 y 2 d 3y2 − 1 2 x 2 ln x 2 1 4 x 2 1 41
12
17. y − 4a
s3 sin x 2 a
19. y − sx 2 1 4 21. y − Ke x 2 x 2 1
33. y − 1 1 e 22x 2 y2
37. Qstd − 3 2 3e 24t ; 3 39. Pstd − M 2 Me 2kt ; M
4
41. (a) x − a 2
(kt 1 21Î 2ysa ) 2
tan21Î 2
(b) t − Stan b
ksa 2 b a 2 b
D
2 b 2 x
a 2 b
_4
35. y − ( 1 2 x 2 1 2) 2
_4
xy=k
4
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