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Unformatted text preview: MA 165 FINAL EXAM 01 Fall 2009 Page 1/9 NAME 10—digit PUID # RECITATION INSTRUCTOR RECITATION TIME LECTURER INSTRUCTIONS 1. There are 9 different test pages (including this cover page). Make sure you have a
complete test. I 2. Fill in the above items in print. Also write your name at the top of pages 2—9. 3. Do any necessary work for each problem on the space provided or on the back of
the pages of this test booklet. Circle your answers in this test booklet. No partial
credit will be given, but if you show your work on the test booklet, it may be used in
borderline cases. 4. No books, notes, calculators, or any electronic devices may be used on this exam. 5. Each problem is worth 8 points. The maximum possible score is 200 points.
6. Using a #2 pencil, ﬁll in each of the following items on your answer sheet: (a) On the top left side, write your name (last name, ﬁrst name), and ﬁll in the little
circles. l (b) On the bottom left side, under SECTION NUMBER, put 0 in the ﬁrst column and then enter the 3—digit section number. For example, for section 016 write 0016, and ﬁll in the little circles. I (c) On the bottom, under TEST/ QUIZ NUMBER, write 01 and ﬁll in the little
circles. (d) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in your
10—digit PUID, and ﬁll in the little circles. (e) Using a #2 pencil, put your answers to questions 1—25 on your answer sheet by
ﬁlling in the circle of the letter of your response. Double check that you have ﬁlled
in the circles you intended. If more than one circle is ﬁlled in for any question,
your response will be considered incorrect. Use a #2 pencil. 7. After you have ﬁnished the exam, hand in your answer sheet and your test booklet to
your recitation instructor. MA 165 FINAL EXAM 01 Fall 2009 Name: 1. The domain of f(:1:) : V1 —1na; is l
2. If f(zc) : 30+ 5, then 3. 11m
m—+0 117—513 1:131 lim
30—)2 ms)  f(2) ___ 50—2 Page 2/9 A.IBS€
B.0<a:§e
C.e<a:
D.0<a:£1
13.133336 1
A.—
2
Be
2 1
C.—
3 3
D.—
4
ED oes not exist A. 1
B. —1
C. 0
D. 2 E. Does not exist MA 165 FINAL EXAM 01 Fall 2009 Name: Page 3/9 4. Find an equation for the line tangent to the curve y : $21n(:v2) at the point Where 117:6. A. y—3ex+62 :0
B. y—6ea:+462 = 0
C. y+em—362 =0
D. y—3€x+262 2 0
E. y+6ex+262 = 0 5. If f’($) = g’(a:) for all cc in (0,00) and f(1) —— 9(1) 2 1, then f(5) — 9(5) 2 6. If y : tan—1(cc2), then A. 5
B. —1
C. 1
D. —5 E. cannot be determined Page 4/9 MA 165 FINAL EXAM 01 Fall 2009 Name: 7. Find the slope of the tangent line to the curve cos msiny : 8. Estimate V 36.3 using a linear approximation at a, : 36. 1
—— at the point ( 2x5 17.2!
3’4' P> H$aa~ .Ucw
$1 .w
Elm A. 6.010
B. 6.015
C. 6.020
D. 6.025
E. 6.030 9. Find the absolute maximum and absolute minimum values of the function ﬂat) 2 22:3 + 3x2 — 121; on the interval [0, 2]. . max20, min —3
. max3, minl max 2, min 0 Upw> . maxO, min—7 E. max 4, min—7 MA 165 FINAL EXAM 01 Fall 2009 Name: Page 5/9 10. A box With square base and open top must have a volume of 4 cubic meters. Find the height of the box that has the smallest possible area. A.h:g
B.h=1
C.h=4
D.h=%
E.h=ﬁ 11. The half~life of a certain radioactive substance is 10 years. How long Will it take for 18 gms of the substance to decay to 6 gms? A. 611110 years B. 10ln6 years ln3
C. 10 R years D. 18 In 10 years ln3
E. 10 E years 12. The graph of the function f(a:) = 3m5 ~— 5$4 has inﬂection points When a: = A. 0 and 1
B. 0 and2
C.1
D.2 E. never MA 165 FINAL EXAM 01 Fall 2009 Name: Page 6/9 13. If f = $5 — 5m + 3, which one of the following statements is true?
A. :1: : 1 is the only critical number of f, and f has a local max. at 1
B. :5 : —1 is the only critical number of f, and f has a local min. at ~1 C. a: = 1, ~1 are the only critical numbers of f, and f has a local max. at —1 and a
local min. at 1. D. x z 1, —1 are the only critical numbers of f, and f has a local min. at —1 and a
local max. at 1. E. a: = 1, —1 are the only critical numbers of f, but f has neither a local max, nor
a local min. at these critical numbers. [—1
+
an: 15. Two sides of a triangle have ﬁxed lengths of 4 meters and 5 meters, while the angle 6 between them is increasing at a rate of 0.06 rad/sec. Find the rate at which the area of the triangle is increasing when 6 = A. 0.6 mZ/sec
B. 0.3 m2/sec
C. 0.3\/§ m2/sec
D. 0.2x/3 mZ/sec
E. 0.6x/5m2/sec MA 165 FINAL EXAM 01 Fall 2009 Name: 1 —1
16/ tan 3: dx:
0 1+$2 PU .0 .U E e 3
17. f (In 2:) da: 2
1 8
P>
('0 #le COII—l 3
18. Find the area of the re ion between the ra h of = ——————
g g p y m
— 2 a: — 2 . " A.
B.
C.
D.
E. E>
=1 A: €11.59?” NM [0 [:3 li w 001* “I H
C) Cb HAM—t Page 7/9 and the m—axis, from MA 165 FINAL EXAM 01 Fall 2009 Name: ___—_____ Page 8/9 _3 3
19. — d :
/_e2 :1: x A. e3 — 66 20. A particle moves in a straight line and its acceleration is given by a(t) : 6t —— 4. Its
initial position is 3(0) = 9 and its position when t = 1 is 3(1) 2 6. Find the velocity
of the particle When t = 2. 21.1fy = :31”, ﬁnd ﬂy— at a: = e.
dsc
A. 1
B. 2
C. 3
D. e E.0 MA 165 FINAL EXAM 01 22. lim
$——>0 x3 Fall 2009 Name: Page 9/9 slum—a: .0 EC 23. The equation 3:3 + 1 : x has exactly one root in the interval (—3, 2). This root is in the interval. 24. The focus of the parabola 312 — 2y — 8m — 23 = 0 is at the point A. (_1, —3)
B. (1, —1)
0. (4,1)
D. (3,1) E. (1, 2) 25. Find an equation of the ellipse with vertices (i3, 0) and foci (21:1, 0). A. 4.752 + 36y2 = 144
B. 8132 + 93/2 = 72
C. 1:2 + 9y2 2 9 D. 9502 + y2 = 9 E. 9:172 + 8y2 2 72 ...
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 Fall '08
 Bens
 Calculus, Geometry

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