Midterm review Answers
(d)
3
y   x2
4
4
19
(b) y  x 
3
3
1. (a)
2. (a)
11. (a)
 (b) 1
(c)
 (d)1
12. 2
13. g(x)=(x+5)/(x+1)
(b)
b, g
(c)
( ,2]
14. (a) -48ft/sec
(b) -64ft/sec
15. No; LHDRHD (left/right hand
derivative)
3. B
4. ~29.5years
5.
(a)
16.
17.
(b) One possible answer:
entire curve
6.
y  x2 ,
FG 20  x IJ
H 3x K
f 1 ( x )   ln
b2,0g  b0, g
18. B
19.
2 x 2  20 x  13
b x  5g
7. One possible answer:
x  13  6t , y  5  3t ,0  t  1
8. C
9. x1.982, x4.301
2
(b) x≠(2n+1)π/6 n integer
3
(c) ,1  [3, )
10. (a)
b
g
2
20x 3  21x 2  20x  12
2
(b) 60x  42 x  20
20. (a)
21. (a)
(b) $480 (c) $1711.11
(d)$3920
35. (a)
(b) (0,11) (c) Vol760.85in3 @
x4.393
22. 10(tanx – 2sinx)/(secx-4)2
23.
V ( x )  2 x 3  57 x 2  385x
6x sec(3x 2 ) tan(3x 2 )
36. E
21
24.
4
37.
25.
y  3x  2
26.
2 x  y cos( xy )
x cos( xy )  1
27.
b g
(c)
2
25 21
 1.818 ft/sec
63
7
2x 
41. (a) 1
1
29. 2 xe 
x
30. Min: 1 at x=0
z FGH
15
40.
x2
42.
Max: 3 at x=1
(b) ( ,0]
[0, )
1
1
(c) , , 1,  (d)
,1
3
3
31. (a)
FG IJ b g FG IJ
H K
H K
(e) Min: -3 at x=0 Max: none
F 1 961IJ , FG1, 35IJ
(f) G ,
H 3 324 K H 12 K
32. D
34.
(b) -4 ft2/sec
39. 180ft
28. C
33.
23
12
38. (a) -80ft3/sec
1
1 x  4
x2 
f ( x)  sin x  e2 x  5x  C
IJ
K
1
dx
x2
(b) 43 (c) 7
3
2
4
43. 27.947
44. (a)
508
7
45. B
46. 19.482
(b) -1
(c) - 4