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Math 151 WIR, Spring 2010, Benjamin
Aurispa
Math 151 Exam 1 Night Before Drill Answer Key
3
1. (a) f 0 (x) = √
2 3x + 7
(b) y − 4 = 38 (x − 3) OR
y = 38 x +
23
8
2. < 14, 2 >
3. (a)
(b)
3
28 ft/sec
3
f 0 (3) = 25
ft/sec
(
x2 − 4
if x ≤ −2, x ≥ 2
2
−(x − 4) if − 2 < x < 2
See Full Solutions for a graph.
Not differentiable at x = −2 and x = 2
4. f (x) =
− 4| =
8
5
√ ,√
89 89
10
8
√ ,√
41 41
5.
6.
|x2
D
√
√
√ E
7. True velocity vector of plane: 150 3 + 10 2, 150 − 10 2
q
√
√
√
Groundspeed = (150 3 + 10 2)2 + (150 − 10 2)2
8. F =< 4, 5 >; |F| =
√
41; θ = arctan
5
4
(where θ is the angle formed with the positive x-axis)
9. Scalar Projection: − √55 ; Vector Projection: < −2, −1 >
10. arccos √
−24
√
34 40
11. 120 J
12. Cartesian equation: x2 + (y − 1)2 = 9; Curve is a circle of radius 3 centered at (0, 1). Direction of
motion as t increases is counterclockwise.
13. x = 8 − 4t, y = 1 + 4t
√
√
14. a = 10, − 10
15. (a)
2
3
(b) −∞
(c) ∞
(d) 0
(e)
D
8
6, 13
E
(f) −4
(g) DNE: lim f (x) = −9 whereas lim f (x) = 9
x→3−
(h)
x→3+
5
2
16. Vertical Asymptote: x = 17 ; Horizontal Asymptote: y =
1
6
7
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Math 151 WIR, Spring 2010, Benjamin
Aurispa
17. Using the Intermediate Value Theorem, there are solutions on the interval (−2, −1) and on the interval
(1, 2).
18. f (x) is not continuous at x = 1 since lim f (x) = 10, but f (1) = 5.
x→1
f (x) is also not continuous at x = 3 since lim f (x) DNE.
x→3
19. No value of m will make f continuous everywhere.
2