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Unformatted text preview: MA 165 Exam 3 01 Fall 2011 NAME W 10—DIGIT PUID W REC. INSTR. _____.___._____ REC. TIME LECTURER W ' 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. No partial credit
will be given. 4. No books, notes, calculators or any electronic devices may be used on this exam. 5. Each problem has 8 points assigned. 4 points are given for taking the exam. The
maximum possible score is 96+4=100 points. 6. Using a #2 pencil, ﬁll in each of the following items on your scantron 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 NUMBER, put 0 in the ﬁrst column and then enter the 3—digit section number. For example, for section 016 write
0016. Fill in the little circles. (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 1~12 on your scantron 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 scantron sheet w your test booklet
to your recitation instructor. ‘ MA 165 Exam 3 01 Fall 2011 Name: Page 2/8 (8 pts) 1. Find the absolute maximum and absolute minimum of the function f(a:) : 39:4 — 4:133 — 12332 + 1 on the interval [—2, 3], Without specifying the value of a: which attains the absolute
maximum or absolute minimum. (8 pts) 2. If f(:c) :
minimum. 53—1 A. absolute max 33
B. absolute max 28
C. absolute max 28
D. absolute max 33 E. NO absolute max $2 A. lecal max at a: = 2
B. local max at a: :2 1
C. local max at :c = 0
D. local max at a: 2: 1 E. local max at a: = O absolute min ~31
absolute min —4
absolute min —31
absolute min 1 absolute min ~35 , then ﬁnd the values of a: at Which f has a local maximum or a local local min at a: = 0
local min at cc : 2
local min at a: = 2 local min at w = 0 NO local min MA 165 . Exam 3 01 Fall 2011 Name: ”m Page 3/8 (8 pts) 3. If 9(33) 2 4:133 — 31:4, which of the following statements are true?
(1) g is decreasing on (1,00).
(2) g has a local minimum at a: = 0. (3) The graph of g is concave downward on (~00, 0). A. (1),(2),and(3)
B. (3) only
C. (1) only
D. (1) and (2) only E. (1) and (3) only (8 pts) 4. Suppose that the second derivative of the function f(:v) is given by
f"(w) = (50 + 3)4(93 + 1)3(~’U — 1)6($ — 3)7($ * 5) How many inﬂection points does the graph of y = f(ac) have ? A. None
B. 1
C. 2
D; 3
E. 4 (8 pts) (8 pts) MA 165 Exam 3 01 Fall 2011 Name: “M Page 4/ 8
5. If f’(x) : g’(:c) for all cc on the interval (0,8) and f(1) —g(1) = 2, then determine the
value for f(5) —— 9(5).
A. 5
B; 2
C. —5
D. 1 E. can not be determined from the above information only 6. Compute the following limit , 62w — 1 — a:
11m —2*
w—>0 :6 Warning: In the numerator, the power of e is 25c and not cc. MA 165 Exam 3 01 Fall 2011 Name: __._____.___ Page 5/8 (8 pts) 7. Compute the following limit A. DNE C.O
D1 (8 pts) 8. Compute the following limit 1, cc 1
m _ —_
m1—+1 a: —— 1 lnx OJIH NIH O 1le MA 165 Exam 3 01 Fall 2011 Name: (8 pts) 9. Which of the following is the graph of the function f (m) : 33:: 9,
A.
B.
C.
D. ? Page 6/8 MA 165 Exam 3 01 Fall 2011 Name: M Page 7/8 2) 9
5 (8 pts) 10. Find the point on the line y = 29: + 3 that is closest to the origin. §
5 CHICO ) (
B<> ——)3,3
§é
6’3
5%
63 U Q (8 pts) 11. Find the area of the largest rectangle that can be inscribed in the ellipse 2 2
w y
—— —=1.
4+9 A. 20
B. 16
C. 12
D. 8
E. 4 MA 165 Exam 3 01 Fall 2011 Name: _________ Page 8/8 (8 pts) 12. A cylindrical can (With both top and bottom lids) is to hold 20000m3 of oil. Find the
radius of the can that will minimize the cost of the metal to manufacture the can. 10
A.
3/7?
1
B. _0
7r
20
C.
D. E
7r
E 3 .599 ...
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