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Unformatted text preview: MA 161 FINAL EXAM 1. The domain of the function \/1 — m — 5 is 2. Which function is graphed below? SPRING 2006 A. [4,5]
B. (3,6)
C. (—5,1)
D. [2,4]
E. [4,6] ln(—:v) atom?
('0
l
H MA 161 FINAL EXAM SPRING 2006 3. One of the following is INCORRECT. Which one? For positive numbers 13,31 A. e$+y = exey B. (ex)?! = 6” C. W=ﬁ+¢gj
D. \/x—=\/E\/37 E. ln(acy) = ylnx 4. Suppose that f +g(:c) = h(m), g(m) = 3 and r: —1. If f is continuous,
then f (2) must be
A. 2
B. —2
C. 4
D. —4 E. There is not enough information to tell for sure MA 161 FINAL EXAM SPRING 2006 5. The horizontal asymptote(s) of the function = 6—3: is (are)
A. y = e
B. y = 0 and y = 1
C. y=0andy=1/e
D. g = 6‘3 E. There is no horizontal asymptote. 6. Consider the secant line of the curve y = 5&2 through the points where x = 2 and
where x = 4. The slope of this secant is muons.»
$03004: MA 161 FINAL EXAM SPRING 2006 7. If cp(t) = x/Eet then (p’(1) = A. 1
B. 26
C. 36/2
D 1/(2x/5)
E. 0 8. In the atmosphere a spherical shock wave, caused by a sonic boom, is traveling out
wards at 1/3 km/ s. At what rate, in km2 / s, does the area occupied by the shock wave
increase, 9 seconds after the boom? (The area of a sphere of radius 7' is 47r7'2.) A. 36%
B. 187r
C. 87r
D. 247r
“ E. 167r MA 161 FINAL EXAM SPRING 2006 __ 71 d sinm _
9. When :13 — —E, 3 — 1113 10. The slope of the tangent line to the curve e“ + cos 7m: + ey + cos 7ry = e + 1 at (1,0) is
A. 71' B. —7r
we 6 5.6.0 —6 MA 161 FINAL EXAM SPRING 2006 11. A radioactive substance has a half—life of 50 days. Initially a sample contains 15 mg. After how many days will only 2 mg remain? 15 In 15
B. 50 111—2 ln(2/15)
ln(1/2)
ln2 I
501n(2/15) ln(15/2) 50 C. 50 D. E. 12. A particle moves along the graph of y = $2 + 3;. When the particle is at the point
(1,2), the :1; coordinate is increasing at 3 units per second. At that moment, how fast is the'distance from the particle to the point (—1,0) changing? A. 6\/§
B. \/§+\/6
C. 12 D. V12
E. 3 MA 161 FINAL EXAM SPRING 2006 13. If f is a differentiable function on (—oo,oo), f(2) = 4, and f(6) = 8, which of the
following statements must be true? I. There is a c in (2, 6) such that f(c) = 6. II. There is a c in (2, 6) such that f’(c) = 6. III. There is a c‘ in (2, 6) such that f’ (c) = 1.
A. OnlyI
B. Only II
C. Only I and II
D. Only I and III
E. Only II and III 14. The absolute maximum and absolute minimum of g(a:) = 3:2 — 23:4 on [—1,1] are A. 1 and 0 B. 1 and —1
C. 1/8 and 0
D. 1/4 and —1
E. 1/8 and —1 MA 161 FINAL EXAM SPRING 2006 15‘ hm cos(2a:) —2c0's(3x) :
x—)0 a: 5/2
—1/2 13/2 swaps?» 1
0 16. A farmer with N ft of fencing Wants to enclose a rectangular region and then divide
it into 3 pens with fencing parallel to one side of the rectangle. What is the largest
possible total area of the 3 pens in ftz? A” Jv2/9
B. Jv2/32
C. N2/20
I). sz/S
E. Jv2/16 MA 161 FINAL EXAM SPRING 2006 17. Suppose F is a continuous function on (—oo,oo). If it has a local extremum at c,
which of the following must be true? I. F’ (c) = 0. II. F’ (c) = 0 or F is not differentiable at c. III. F”(c) yé 0.
A. OnlyI
B. Only II
C. Only III
D. Only I and II
E. Only II and III A. —ln(1+:1:2)+ln2
B. 1/(1+a:2) C. wZ/(1+a:2) D. 2x/(1+$4) E. 41:3/(1+a:2) 10 7r/ 2
20. / cos 3tdt =
0 FINAL EXAM 11 SPRING 2006 EUQW? mung!» —5/8
—3/8
—45/16
—1/2
1/2 —1/2 1/3
_1/3 MA 161 FINAL EXAM SPRING 2006 21. If h” 2 695(1: — 1)3(:I: + 2), ﬁnd all open intervals where h is concave down.
A. (0,1) ‘
B. (—oo,0) and (1,00)
C. (—2,0) and (0,1)
D. (—2, 1)
E. (—00, —2) and (1,00) 22. Find all Open intervals where 90(13) = g is increasing.
A. (—oo,0)
B. (—00, —\/§) and (—\/§,0)
0 (x/§, ﬂ)
D. (0, and (V100)
E. (0,00) 12 MA 161 FINAL EXAM SPRING 2006 23. If f”(:c) = 617+ 2, f(1) = 2 and f’(1)= 4 then f(3) = A. 18
B. 30
C. 34
D. 8
E. 22 4 5 ' 5
24. If / g(t)dt=2and / g(t)dt=6, then / g(t)dt=
2 2 4 B4 D. 8
E. 12
13 1
25. / arm/1 +3162 d2: =
0 14 A. 2 B. 2/3
c. 1/3
D. 7/9
E. 5/6 ...
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This note was uploaded on 09/14/2011 for the course MATH 16100 taught by Professor Juan during the Spring '10 term at Purdue UniversityWest Lafayette.
 Spring '10
 JUAN

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