# 161FE - MA 161 &: 161E FINAL EXAM December 2003 ' Name...

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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 University-West Lafayette.

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161FE - MA 161 &: 161E FINAL EXAM December 2003 ' Name...

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