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Unformatted text preview: MA 161/161E I Final Exam Spring 2007
Name: 10—digit PUID: Lecturer: Recitation Instructor: Recitation Time: Instructions:
1. This package contains 25 problems worth 8 points each. 2. Please supply all the information requested. On the scantron sheet, print your
name, your divisionsection number, and 10 digit PUID number in addition to ﬁlling
in the corresponding circles. 3. Work only in the space provided, or on the backside of the pages. Circle your
choice for each problem in this booklet, and mark your answer on the scantron sheet. 4. N0 books, notes, calculator, or any electronic devices may be used on this exam. M 7A {(3 M 106 HG {1133A 14A 19% MD (7A (ED WC am) a! e“ 2.2 E" 2% B 24 E ’2' 37? MA 161 Final Exam 1. Consider the set of points (:13, y) satisfying the equation
$2+y2—4cc—4y+7=0. Which of the following statements are true?
I. It meets the x—axis.
II. It meets the yaxis.
III It includes the point (0,0). 2. f and g are functions deﬁned on the entire real line and f
decreasing. Which of the following statements are true? I. g o f is decreasing;
II. 9 o f is increasing.
III. f o g is decreasing. IV. f o g is increasing. Spring 2007 A. Only I and II
B. Only II and III.
C. Only I and III.
D. All of them. E. None of them. is increasing while 9 is A. Only I. B. Only II. C. Only II and IV.
D. Only I and III.
E. Only III and IV. MA 161 Final Exam Spring 2007 w — 1
3. What is the domain of the inverse function f1 if f(a:) = e. 2 ? A. (~oo,oo)
B. (0, 00) C. (2,00) D. (1/2,oo) E. (—1/2,oo) 4. Which of the following limits exist?
A. Only I. B. Only II. C. OnlyI and II. '
D. Only II and III.
E. None of them. ‘ I. _Iimx_,0+(1 + el/$)_1.
II. limH0_(1 +e1/m)1.
III. Iimwou + el/w)"1. MA 161 Final Exam' Spring 2007 5. What is
lim cos“1(ﬁ_ 1) ?
m—)0+ cc — 1 (Here, cos"1 refers to the inverse function of cosine.)
A. O
B. 1
C. 7r/ 3
D. 7r/ 6 E. It does not exist. 6. Let f(:r) = %x3 + 11:2 + 256 — 1. Which of the following statements are true? I. The intermediate value theorem guarantees that f (51:) : 0 has a solution in the
interval [—2, 2]. II. The mean—value theorem guarantees that f (x) = 0 has at most one solution in
["27 2] ' A. Only I.
B. Only II.
C. Both. D. Neither. E. None of the answers
above is correct. MA 161 Final Exam Spring 2007 7. Which of the following functions are continuous? I. The distance from the latinch pad of a rocket sent into space, as a function of
time. II. The price of postage for sending a letter from West. Lafayette to New York City
as a function of the weight. III. The taxi—fare in West Lafayette as a function of the distance traveled.
A. Only I. B. Only II. C. Only III. D. Only I and II.
E. Only II and III. 8. Which of the following statements about the function Va: + 1 ~ V; are true?
I.‘ It is deﬁned on the interval (—1, 00). II. It has a horizontal asymptote. A Only I
III. It has a vertical asymptote. B Only 11
C. Only III. D. Only I and III.
E. All of them. MA 161 . Final Exam 9. Let f(:17)= sin(2x). What is f(66)(0)? 10. What is the derivative of (new at a: = 1? Spring 2007 A. 0 B. 1 C. —1 D. 71' E. None of the above. A. 0 B. l C. e D. ln(e) E. None of the above. MA 161 _ Final Exam Spring 2007 11. Let f (as) = W. What is the domain of its derivative f’ (x)?
I A. [1,00)
B. (1,00)
C. (—1,1)
D. [~1,1]
E. (—oo,1]. ‘12. Let L be the tangent line to «E + \/37 = 1
at the point (1/4, 1/4). Which of the following lines is parallel to L?
A. y = (1/4)::: + 2
B. x — y = 1
C. y = 0
D. 7ry + 7m: 2 13
E. None of the above. MA 161 Final Exam Spring 2007 13. What is the derivative of
y __ sin2(:1:) tan4 (a:) $2
at a: : 7r/4?
A. 80/7r2 — 64/7r3
B. 7r2/6
C. 1
D. 1007r — 6/7r2 E. None of the above. 14. If the area of a rectangle grows at 20 in2 / min and its base grows at 2 in/ min, at what
rate is the height growing when the base is 8 in and the height is 6 in? A. 1 in/min
B. 2 in/min
C. 6 in/min
D. 20/7 in/min
E. 10 in/min MA 161 Final Exam Spring 2007 15. HOW many local minima. does
3 — sin(:c) have on (0, 2w)?
A. 0
B. 1
C. 2
D. 3
E. 4 '16. The function 1174 + 2x3 — 4 is concave up on I A. (—00, 0)
B. (—00, 1)
C. (—1,1)
D. (0,00)
E. (—1, 0) MA 161 . Final Exam Spring 2007 17. Emma, em in(1'+ 6“”) 2
A. 1
B. 0
c. —1
D. 00 E. —oo 18. The sum of three positive numbers is 12. If one of them is three times another, What
is the maximum possible value for the prodﬂct of these three numbers? A. 24
B. 56
C. 42
D. 48
E. 62 MA 161 Final Exam Spring 2007 19. To approximately solve the equation 11:3 — 2x + 6 = 0 by Newton’s method, we start
with the initial guess $1 = 2. Then :52 = A. —1
B. 0
C. 1
D. 3/2
E. 5/2 20. If g’($) : :17 +% and 9(1) :1, then 9(3) =,
I A. 3
B. 3/2
C. 3ln3/2
D. 5+ln3
E. 2+1n3 10 MA' 161 Final Exam 21. If [30 f(a:)dac = —3 and f: f(x)d:c := 5, then f: f(:c)dx = Spring 2007 A.2
B.0
0.3
D.5
E8 22. Suppose f is a continuous function on (—00, 00) and ff f (t)dt = g(:c). Which is true? 1 9’03) = f (50)
II. If f (11:) > 0 for all as, then g(:z:) is an increasing function. III. If h(:c) = g(x2), then h’(1) = 2f(1). 11 A. Only I. B. Only II. C. Only III. D. Only I and II.
E. All are true. MA 161 Final Exam _. ‘ 3
23. / (1—m2)da::
0 .24. Which substitution should be used to evaluate fsin(x)e°°s(”)dx? 12 Spring 2007 A. ——9 B. —6 C. —8 D. 4 E. 9 A. u = sin(m) B. u = cos(a:) c. u : 6mm D. u = e— cos<w>
E. u = —e—C°S(") MA 161 Final Exam Spring 2007 25. 1: minutes after being ﬁlled, a bucket leaks water at the rate of 1
(t + 1)2 ﬂuid ounces per minute. HOW much water (in ﬂuid ounces) Will be lost in the ﬁrst 9
minutes? A. 4 B. 1 / 10 C. 9 D. 10 E. 9/10 13 ...
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