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

Appendix I Answers to Odd-Numbered Exercises A121
3. (a), (c) y
5. (a), (c)
(_3, 2)
r(_1)
rª(_1)
0 x
y
3c3 Ans rª(0) 10.2.3
09.13.04
(1, 1)
(b) r9std − k1, 2t l
(b) r9std − 2e 2t i 1 e t j
21. 6t 2 ys9t 4 1 4t 2 d 3y2 23.
s6
2s3t 2 1 1d 2
25. 1 7 s 19
14 27. 12x 2 ys1 1 16x 6 d 3y2
29. e x | x 1 2 | yf1 1 sxe x 1 e x d 2 g 3y2
31. (2 1 2 ln 2, 1ys2); approaches 0 33. (a) P (b) 1.3, 0.7
35.
y=k(x)
4
y=x–@
0
r(0)
7. (a), (c) y
2
rª(3π/4)
x
”2œ„2, œ„2’
r(3π/4)
0 4 x
(b) r9std − 4 cos t i 1 2 sin t j
1
9. r9std −K 3L
2st 2 2 , 0, 2 2 t
11. r9std − 2t i 2 2t sinst 2 d j 1 2 sin t cos t k
13. r9std − st cos t 1 sin td i 1 e t scos t 2 sin td j
1 scos 2 t 2 sin 2 td k
15. r9std − b 1 2tc 17. k 2 7, 3 7, 6 7 l 19. 3 5 j 1 4 5 k
21. k1, 2t, 3t 2 l, k1ys14, 2ys14, 3ys14 l, k0, 2, 6t l, k6t 2 , 26t, 2 l
23. x − 2 1 2t, y − 4 1 2t, z − 1 1 t
25. x − 1 2 t, y − t, z − 1 2 t
27. rstd − s3 2 4td i 1 s4 1 3td j 1 s2 2 6td k
29. x − t , y − 1 2 t , z − 2t
31. x − 2 2 t, y − 1 t, z − 2t
33. 66° 35. 2 i 2 4 j 1 32 k
37. sln 2d i 1 sy4d j 1 1 2 ln 2 k
39. tan t i 1 1 8 st 2 1 1d 4 j 1 ( 1 3 t 3 ln t 2 1 9 t 3 )k 1 C
41. t 2 i 1 t 3 j 1 ( 2 3 t 3y2 2 2 3) k
47. 2t cos t 1 2 sin t 2 2 cos t sin t 49. 35
Exercises 13.3 • page 868
1. 10s10 3. e 2 e 21 5. 1 27 s13 3y2 2 8d
7. 18.6833 9. 10.3311 11. 42
13. (a) sstd − s26 st 2 1d;
rstssdd −S4 2
D s i 1S 4s 1 1D j 1S 3s 1 3D k
s26 s26 s26
(b) S4 2 4
s26 , 16 12
1 1, 1 3D
s26 s26
15. s3 sin 1, 4, 3 cos 1d
17. (a) k1ys10 , (23ys10 ) sin t, (3ys10 ) cos tl,
k0, 2cos t, 2sin t l (b) 3 10
1
1
19. (a)
e 2t 1 1 ks2et , e 2t , 21l,
e 2t 1 1 k1 2 e 2t , s2e t , s2e t l
(b) s2e 2t yse 2t 1 1d 2
37.
_4 4
z
5
0
_1
3c3 Ans 10.3.29
9.13.04
_5 0
250
0 50
500 x
100
y
39. a is y − f sxd, b is y − sxd
41. std − 6s4 cos2 t 2 12 cos t 1 13
s17 2 12 cos td 3y2
k(t)
0 2π 4π 6π
t
(t)
0.6
_5 0
5 t
integer multiples of 2
43. 6t 2 ys4t 2 1 9t 4 d 3y2
45. 1y(s2e t ) 47. k 2 3 , 2 3 , 1 3 l, k2 1 3 , 2 3 , 22 3 l, k2 2 3 , 1 3 , 2 3 l
49. x 2 2z − 24, 2x 1 z − 2
51. (x 1 5 2 ) 2 1 y 2 − 81 4 , x 2 1 (y 2 5 3 ) 2 − 16 9
7.5
53. s21, 23, 1d
55. 2x 1 y 1 4z − 7, 6x 2 8y 2 z − 23
65. 2yst 4 1 4t 2 1 1d 67. 2.07 3 10 10 Å < 2 m
Exercises 13.4 • page 878
1. (a) 1.8i 2 3.8j 2 0.7k, 2.0i 2 2.4j 2 0.6k,
2.8i 1 1.8j 2 0.3k, 2.8i 1 0.8j 2 0.4k
(b) 2.4i 2 0.8j 2 0.5k, 2.58
5
5
2.5
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