360
FINAL EXAM ANSWERS TO CHAPTER TEST FORMS
(d)
34. 4e2+2 35. 1 cos(2x )+ C ) + xsin(2x 2 36. −e cot(t ) + C 2 ⎞ +6x lnx − x − 6 x + C ⎟⎟ ⎜⎜ 4 ⎠ ⎝ 2 38. −2ln x + C
37.
⎛x2
56. 1126.12 lb 57. y = Ce−12x+ C2ex 1
39. 72
3t ; 58. xt( ) = − Ce5t − 5Ce− y (t ) = 2Ce−23t 1 2
40. 4 41.
5πe25(e35− 1)
59. 2 13
42. Divergent
60. 0.694915
43. Convergent1 3, ⎡ 2 −11⎤ 44. ⎢ 30 −5⎥⎥ ⎢− ⎢ 8 −3⎥⎦ ⎣− 45. 14; invertible
46.
61. (a)
8 5
(b)
2 5
2 , or 2 6, or 0.3266 3 15
62. 0.6326 63. 0.08192
⎡−⎤ ⎡−2⎤ r=7, t ⎢ 2 ⎥ ; r = 4, t⎢⎥ ⎣ 3⎦ ⎣0⎦
64. 3x2 + x + 2xln 6=5. k
47. (a) ⎡⎢ 480 ⎤⎥ ⎣168 ⎦
x
0.871342
66. 6.66
672 ⎤ (b) ⎡⎢ ⎥ 307.2 ⎣ ⎦
FINAL EXAM, FORM D
48. 4 y + 3xy2
1. y =−3 x + 19 2
49. 3 y2
2. 6 x + 3h − 1 3) ⎤ ( (2x2 )+x +6x ⎥ ⎥ 2xe2y cos cos( ) (e2yx) ⎥
⎡ 2 6 y ( x + 3) ⎢ 50. ⎢ 2y e2yx ⎢⎣e
2
=2 at (0,0) . 51. Relative minimum
⎦
3. 1.96 4. Amplitude: 3; period:π ; mid-line:y =−2 ; 2 maximum: 1; maximum: −5. 5
52. 2e4 − 2e2 +2
53. y = Ce2x6 3
, or y=
3 2
6
eCe2x 3
54. y =sinx−x 2 + 4 55. (a)
y
4
y = 0,2
(b) Unstable, asymptotically
x
1 −5
−4
−3
−2
−1
−1 −2
x 1
−3 −4 −5
(c) y = 1
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