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Unformatted text preview: MA 161 &: 161E FINAL EXAM December 2003 ' Name Student ID Number Lecturer Recitation Instructor INSTRUCTIONS: 1.
2. Fill in all the information requested above and on the scantron sheet. This booklet contains 23 problems, each worth 8.5 points. You get 4.5 points for
coming; the maximum score is 200 points. For each problem circle the answer of your choice, and also mark it on the scantron
sheet. . Work only on the pages of this booklet. . Books, notes, calculators are not to be used on this test. At the end turn in your exam and scantron sheet to your recitation instructor. MA 161 & 161E FINAL EXAM December 2003 1 1' z—x —
'z—lgl+ x2—5x+6_ A. —4 B.oo D.1
E.O . . 1
2 53:, m;— A. 00 B2
0.1
D.O E. limit does not exist MA 161 & 161E FINAL EXAM ' December 2003 d
3. 3;(slns)= A. Ins B. 1 +1113
1113 C.— s
D.1 E. (s+1)1ns 4. The 47th derivative of f (z) = cos 2a: is A, _ sin 23; —247 sin 21: sin 21: 247 sin 21: 553.0?“ —247 cos 2a: MA 161 86 161E 5. If we” — yea’ = 7r then dy/dx = 6. If g(t) = f(sint) then 9’“) = FINAL EXAM December 2003 E
2:
7r + ye":
may
ye‘” + e”
me?! + e“; a: —e
D. y
x—ey ye“ —— 69
me?! — cm A. f(cost) B. f’(cost) C. f’(sint)+cost
D. f’(sint)cost
E. f(sint)cost MA 161 &: 161E FINAL EXAM December 2003 2
1+3 7. The slope of the tangent line to the curve y = , at the point Where a: = ——2, is A. —2
B. —1
C. 0
D. 1
E. 2 8. Consider the following statements for a function f (cc) deﬁned for —00 < cc < 00:
I. If f is differentiable at —3 then it is continuous at —3. II. If f is continuous at —3 then f (—3) = lim3 f
z—r—
III. If f (—3) = lim3 f(:c) then f is continuous at —3.
3—»— Which is true? A. Only I B. Only II
C. Only I and II
D. Only II and III
E. All three are true MA 161 86 161E FINAL EXAM December 2003 9. On the ﬁrst day of Christmas (at 8 a.m.) my true love gave me 10 grams of radioactive
substance. On the fourth day of Christmas (again at 8 a.m.) I had 3 grams left. What is the half—life of that substance, in days? 10. If 2 1/43 then 9'“) = 11110/3
4
ln8
1n 10/3 C. 2
10 In 2
3
E. Not possible to determine A. B. D. thlr—I B. —— C. 1n4 D. —1n4
_1n_2 MA 161 & 161E FINAL EXAM December 2003 11. A particle moves along a line a: = y. When it reaches the point (1, 1), its a: coordinate
increases at rate 3 ft/s. At what rate, in ft/s, does its distance to the point (1,0) change at this moment? 12. Linear approximation gives for v3 24 the value A. \/§
B. Ni
O. 3 D. .3\/§
E. 6 www
ﬂ!“ spam?
[\3 to
who Gala! colon MA 161 85 161E FINAL EXAM December 2003 13. The maximum of (1 — x)em on (—1, 1) is
A. 0
B. 1
C. 2/e
D. 26
E. e 14. Suppose an everywhere differentiable function h satisﬁes h(2) = 4, h(5) = 6. The
mean value theorem implies that there is a A. c in (4,6) such that h’(c) = 2/3
B. c in (4,6) such that h’(c) = 3/2
C. c in (2,5) such that h’(c) = 2/3
D. c in (2,5) such that h’(c) = 3/2
E. c in (2, 5) such that h’(c) = 5 MA 161 85 161E FINAL EXAM _ December 2003 15. If <p”(:l:) = (:1: — 1)2(:1: + 1), the graph of <p can be
A. ' B. 16. If g’(:1:) = 2:2 — 1, 9(2) 2 1/3 then g(0) = T A. 1/3 B. o C. 1/2
I D. 2/3 MA 161 & 161E FINAL EXAM December 2003 17. For F a differentiable function on (—00, 00) and c a reallnumber, which statement is
true? I. If F has a local maximum at c then F’ (c) = 0.
II. If F’ (c) = 0 then F has a local maximum or minimum at c.
A. Neither is tirue
B. Only I is triue
C. Only II is true
D. Both are tﬁue E. None of the above answers is correct 18. 233(22' — 1)2 = I... A. 7
B. 15
C. 22
D. 27
E. 35 10 MA 161 85 161E FINAL EXAM ! December 2003
4 d2: 19' 1/ $73: A. 16 B. 8
 C. 6 D. 3
l
i

I
I
l
i
2 2 5 i
20.If/f(a;)d:1:=3and/f(x)dx=4then/f(x)dx= i A. _7
3 5 3 I
l B. —1
C. 1 D. 7 E. 12
 11 MA 161 & 161E FINAL EXAM December 2003 21. If2/)(:1:) ={ A. 1
B. 1
C. 2
D. 26 E. 2e+1 e
1 ifx<1
’ — th d:
1/:1:,if:1:>1 (en/1pm)“;
o NIH 22:2 .
22. If J(:1:) = /(lnt)1/2dt then J’(e) = A_ 0
3 B. 1
a C. ﬂ — 2e1n2 D. 1114 — e\/§
E. 4cm — 1 12 MA 161 85 161E FINAL EXAM 13 December 2003 ...
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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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