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

Appendix I Answers to Odd-Numbered Exercises A77
37. (a) e x sx 3 1 3x 2 2 x 2 1d
(b) 2
10
39. (a) f 9sxd −
(b) 4
_6
f
f
fª
_2
4x
sx 2 1 1d ; f 99sxd − 4s1 2 3x 2 d
2 sx 2 1 1d 3
f·
_2
fª
41. 1 20
4 43. (a) 216 (b) 2 9 (c) 20 45. 7
47. y − 22x 1 18 49. (a) 0 (b) 2 2 3
tsxd 2 xt9sxd
51. (a) y9 − xt9sxd 1 tsxd (b) y9 −
xt9sxd 2 tsxd
ftsxdg 2
(c) y9 −
x 2
53. Two, s22 6 s3, 1 2 s1 7 s3dd 55. 1
57. $1.627 billionyyear
0.0021
59.
s0.015 1 [S]d ; 2
The rate of change of the rate of an enzymatic reaction with
respect to the concentration of a substrate S.
61. (c) 3e 3x
63. f 9sxd − sx 2 1 2xde x , f 99sxd − sx 2 1 4x 1 2de x ,
f -sxd − sx 2 1 6x 1 6de x , f s4d sxd − sx 2 1 8x 1 12de x ,
f s5d sxd − sx 2 1 10x 1 20de x ; f snd sxd − fx 2 1 2nx 1 nsn 2 1dge x
Exercises 3.3 • page 196
1. f 9sxd − x 2 cos x 1 2x sin x 3. f 9sxd − e x scos x 2 sin xd
5. y9 − sec ssec 2 1 tan 2 d
7. y9 − 2c sin t 1 tst cos t 1 2 sin td
9. y9 − 2 2 tan x 1 x sec2 x
s2 2 tan xd 2 11. f 9sd −
13. y9 − st 2 1 tdcos t 1 sin t
s1 1 td 2
15. f 9sd − 1 2 sin 2 1 cos 2
21. y − x 1 1 23. y − x 2 2 1
25. (a) y − 2x (b)
3π
2
6
2
π
” , π’
2
1
1 1 cos
31. (a) f 9sxd − s1 1 tan xdysec x (b) f 9sxd − cos x 1 sin x
33. s2n 1 1d 6 1 3, n an integer
35. (a) vstd − 8 cos t, astd − 28 sin t
(b) 4s3, 24, 24s3; to the left
37. 5 ftyrad 39. 5 3 41. 3 43. 23 4
45. 1 2 47. 21 4 49. 2s2 51. 2cos x
53. A − 2 3
10 , B − 2 1
10
55. (a) sec 2 x − 1
cos 2 x
(c) cos x 2 sin x − cot x 2 1
csc x
57. 1
Exercises 3.4 • page 204
(b) sec x tan x − sin x
cos 2 x
4
e sx
1.
3. sec 2 x 5.
3s 3 s1 1 4xd 2 2sx
7. F9sxd − 24 x 11 s5x 3 1 2d 3 s5x 3 1 1d
5
9. f 9sxd −
2s5x 1 1
11. f 9sd − 22 sin s 2 d
13. y9 − xe 23x s2 2 3xd 15. f 9std − e at sb cos bt 1 a sin btd
17. f 9sxd − s2x 2 3d 3 sx 2 1 x 1 1d 4 s28x 2 2 12x 2 7d
19. h9std − 2 3 st 1 1d21y3 s2t 2 2 1d 2 s20t 2 1 18t 2 1d
21. y9 −
1
2sx sx 1 1d 3/2 23. y9 − ssec2 d e tan
25. g9sud − 48u 2 su 3 2 1d 7
su 3 1 1d 9 27. r9std −
29. H9srd − 2sr 2 2 1d 2 sr 2 1 3r 1 5d
s2r 1 1d 6
31. F9std − e t sin 2t s2t cos 2t 1 sin 2td
33. G9sxd − 2Csln 4d 4C/x
4e 2x
x 2
sln 10d10
2st
1 2 e2x
35. y9 −
sin
s1 1 e 2x d 2 1 1 e 2x
37. y9 − 22 cos cotssin d csc 2 ssin d
39. f 9std − 2sec 2 ssecscos tdd secscos td tanscos td sin t
41. f 9std − 4 sinse sin 2t d cosse sin 2t d e sin 2 t
sin t cos t
43. t9sxd − 2r 2 psln ad s2ra rx 1 nd p21 a rx
45. y9 − 2 cosstan xd sec2 sxd sinssinstan xd
2ssinstan xd
47. y9 − 23 cos 3 sinssin 3d;
y99 − 29 cos 2 s3d cosssin 3d 1 9ssin 3d sinssin 3d
2sec t tan t
49. y9 −
2s1 2 sec t ;
y0 − sec t s3 sec3 t 2 4 sec 2 t 2 sec t 1 2d
4s1 2 sec td 3/2
51. y − sln 2dx 1 1 53. y − 2x 1
55. (a) y − 1 2 x 1 1 (b) 3
st
27. (a) sec x tan x 2 1
29. cos 1 sin ; 2 cos 2 sin
0
ms80171-1
6et 3.3.25b
6.24.06
π
(0, 1)
_3 3
_1.5
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