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Unformatted text preview: MA 165 FINAL EXAM Fall 2007 Page 1/8 NAME
10digit PUID #
RECITATION INSTRUCTOR
RECITATION TIME LECTURER INSTRUCTIONS 1. There are 8 different test pages (including this cover page). Make sure you have a
complete test. 2. Fill in the above items in print. Also write your name at the top of pages 2—8. 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. 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. (b) On the bottom left side, under SECTION, write in your division and section
number and ﬁll in the little circles. (For example, for division 9 section 1, write
0901. For example, for division 38 section 2, write 3802). (c) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in your
10—digit PUID number, and ﬁll in the little circles. ' ((1) 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 Fall 2007 Name: _____ Page 2/ 8 1. lim $l“2:
:c—)2 33+2 A. —1
B. 0
C. 1
D. 00
E. Does not exist _ 3
2. 11m 6 22
95—)2+ scam?
G5
I
00 Does not exist 3. The domain of f(x) = ln (177:2) is A. (1,00) B. (0,1) C. (—oo,0) D. (1,00) and (—oo,0)
E. (£300) and (—00,0) 4. For What value of c will f be continuous for all x, if 2x+1, forxgc
f(:v)= ~x+2, forx>c .0 1 B. —2 1 C. — 3 1 D. — 4 E. for 110 value of c MA 165 FINAL EXAM Fall 2007 Name: __—__ Page 3/8 1 a: 5.3151311 x—l Does not exist 6. If f(:r:) = $2 lnx, then f”(x) = $+ 21,1111, 3+21na: 393+21na: 3+2xlnx
1 517 magma? . , d
7. The equatlon y2 Ina: + y = 2:0 deﬁnes y as a function of as. Compute _y at da:
(W!) = (1,2)
A. 0
B. 2 C. —§ D. ——4
E. —2 8. Sand falling at the rate of 3 ft3/ min forms a conical pile whose radius is always twice
the height. The rate at which the height is changing when the height is 10 feet is MA 165 FINAL EXAM Fall 2007 Name: _____ Page 4/8 4
9. The function f (ac) = a: — — has a $2 relative max at m = 2 relative min at a: = 2
relative max at a: = —2 relative min at $8 = —2 93.6.0th none of the above 1 1 1
10. The graph of y = E m4 —— g $3 + ~2— x2 has how many inﬂection points? A. None
B. 1
C. 2
D. 3
E. 4 3 11. The maximum slope of the curve y = 6x2 — a: is A. 16 B. 2
C. 6
D. 4
E. 12 12. If the highest point on the curve 3/ : K — x2 — 4:1: is on the xaxis, then K =: A. 0
B. —4
C. —2
D. 1 E3 MA 165 FINAL EXAM Fall 2007 Name: _____ Page 5/8 1
4 13. A linear approximation shows that (16.2) is approximately 14. Let P be the point on the curve y = «E that is closest to (5,0). The sis—coordinate of
P is E .U Q P3 ?>
ﬁwlﬁ‘mlomww 15. An observer 3 miles from the launch pad watches the shuttle go straight up. He
measures the angle between the horizontal and his line of sight to the shuttle. When that angle is 2, it is increasing at the rate of % radians/sec. How fast is the shuttle
rising at that instant (in miles/ sec)? A. 2 B. 1.5 C. 1 D. 1.2 E. 1.75 MA 165' 1
16. /
0 17. lim IB—)0 1
18. /
1 FINAL EXAM 2
136“” d3: = cosx— 1 Fall 2007 1
——dx= 1 — 1:2 sin— 1 ' 5L” 0
19. / xx/m+ ldac =
—1 Name: scam? macaw)» papaya? 1113
1n2
21n2
1114 21113 El“ 51* col» mm om: MA 165 FINAL EXAM Fall 2007 Name: —_ Page 7/8 ‘5 2
20. If Fa) = / et dt, then m4) = 2
0 a; A
MW” (0 91:19.03?
as!“ *l 21. If f(x) = (ln$)$, then f’(e) = ('6le scam?»
Ch [0 1 1 + 2 and the x—axis, from m = 1
a: 22. The area of the region between the graph of y =
to at = M3 is .tn .6 .0 .w .>
3: 5: Na ml: co=1 23. The half—life of a radioactive substance is 80 years. In how many years will its mass
decrease to % of its original size? 11180
. 2 —
A ln2 1112
B. —
5 ln5 ln5
. 4 —
C 0 ln2 ln2
D. 4 —
0 ln5 ln5
E. 80 m MA 165 24. The focus of the parabola m2 + 2:1: —— y + 3 2 0 is at FINAL EXAM Fall 2007 Name: 25. The ellipse 92:2 + 4312 — 3691: + 8g + 4 = 0 has vertices at the points A. (2, —¢5) and (2, x/g)
B. (—2, —4) and (—2,2)
C. (—2, 1) and (—2,6)
D. (—4, 2) and (2,2) E. (2, —4) and (2, 2) ...
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