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20111207084809187

20111207084809187 - MA 165 Exam 3 02 Fall 2011 NAME...

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Unformatted text preview: MA 165 Exam 3 02 Fall 2011 NAME 10—DIGIT PUID smuflows l REC. INSTR. ____.___.____.___ REC. TIME LECTURER INSTRUCTIONS: 1. There are 8 difierent test pages (including this cover page). Make sure you have a complete test. V 2. Fill in the above items in print. Also write your name at the top of pages 2—8. 3 r 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 1 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 02 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 aid your test booklet to your recitation instructor. MA 165 Exam 3 02 Fall 20 1 1 Name: Page 2/8 (8 pts) 1. Find the absolute maximum and absolute minimum of the function f($) = 3:124 — 43!:3 — 12932 + 1 on the interval [~3, 3], Without specifying the value of as which attains the absolute maximum or absolute minimum. 1" t . l?) '2, f" 4: {fl} '2' 421% w 22 >4 W #114 ‘34 r 22x (23x «2) (8 pts) 2. If f(:c) = so minimum. A. absolute max 33 B. absolute max 28 33K C. absolute max 244 D. absolute max 33 E. NO absolute max A. local max at a: = 2 B. local max at a: = 2 9%” C. local max at :c = 0 D. local max at :1: = 0 E. local max at cc 2 0 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 :c = 0 local min at a: = 4 local min at a: = 4 local min at :v : 2 NO local min MA 165 Exam 3 02 Fall 2011 Name: (8 pts) 3. If g(a:) = 33:4 —— 41:3, which of the following statements are true? (1) g is increasing on (1, oo). ‘ (2) g has a local minimum at a: = 0. 2 (3) The graph of g is concave downward on (0, g). / _ 2 7: 1 , _ _ a”. o - H;O+r+‘~+- > ‘3 (it) " “’5” ’1. V B. (3) only <31) {,7 '1'?" WA: (2) (n W491 CY OJ» C. (1) only ” “-1;er 1.1,r 041W): “9‘7 ‘16 ‘24y 1. “M 5,5 (3)“ 2) D. (1) and (2) only ” - ' —~ ~~ 0 + + ~k+ and wave y 9f E. (1) and (3) only C) .11— 3 (3) 3/; TV Lu (8 pts) 4.. Suppose that the second derivative of the function f (cc) is givendby o > 2'0 ‘2 f”(a:) = (a: + 393(2: + 1)2(kci;i‘)5(ac — 3)6(a: — 5)4. How many inflection points does the graph of y = f (:3) have ? , .._. ...= O ifs/”w own ”it? 3,,” was? A- None I; 1 B. 1 756 C. 2 D. 3 E. 4 Page 3/8 MA 165 (8 pts) 5. If f’(m) : g’(a:) for all a: on the interval (0, 9) and f(1) value for f(6) — Them fo}: :lfc'y)» [(51)=O Exam 3 02 9(6)- A.5 B.4 >60. 3 D2 Fall 2011 Name: Page 4/8 _ 9(1) : 3, then determine the E. can not be determined from the above information only 14175 HY) =23{v)»%€><) 107.1%”) :3 :11?) ”(15%) ":3 (8 pts) 6. Compute the following limit _ 63‘” — l —— a: 11m ‘—'—-— m—rO £132 Warning: In the numerator, the power of e is 333 and not 2:. 13" n UH , “‘2 39‘ Am C if): :1 91m “’5’“ ”i o NW M2 M 1 \ ,«f’ “BX Q Jill-Y H CW 3'6 21». :2: 9‘9 x-u» G G A O ‘59 I _ 4W3 55“.,”‘1 “,7 Z- ‘ egiiwk», Lil) .x'n 3'6 ”—71 .i,‘ t: “(33 p7“ 'XL _, x-mC'“ 2%)“? fl ,X—fl)‘ ,0 “ O f 9‘!“ A. DNE B. _ MA 165 Exam 3 02 Fall 2011 Name: Page 5/8 (8 pts) 7. Compute the following limit 2: QM 2 ,2 Mm ,? 3 Zj+§l):"€ { : me0+ A 0 r B l “m 2. QA‘W VL"“{H“:7> __ €19- (‘ “L ‘” vn‘éw" “ C Mae-e0 X f: 6 - I QM §+fi \ 96D 62 (Am XQmO-t?) :E‘W’ (“31”: \ PM (Xmm 3;; E. DNE A. L’r+ I _,. Q 3 by.” «L’TL CE m£:%i2 ____ u 2 LIV“; K L :- Xv-rm ”If/(1 “H XHQG I“??? (8 pts) 8. Compute the following limit km a: — 1 m~—->1 113*]. 11137 km .23.... .. L27tflfl‘m me—th XHL\X‘“? 3M3“ Mug“? (X‘PJ‘Q'Y‘X A 0 (Do u“ 613 L 1 L’H ‘ i o B' Z _;_ film x- zjfiizL Ami (x474;— HW C 3 I all 3 j ’m _M§:iz:r:,_.i :5 ”will. Aw}, 3-4. Wu Wei gel; 9% D 3 i7; 2 0 " . PM 2* MA 165 Exam 3 02 Fall 2011 Name: ___—____ Page 6/8 (8 pts) 9. Which of the following is the graph of the function f(a:) = 2 + 9 ?y a: A_ ' R 583mm @323ng V3 (mi; 3:3 0 HR fiii B. a \<" I 1/ \ I 1 l C. D. (8 pts) (8 ptS) MA 165 Exam 3 02 Fall 2011 Name: Page 7/8 10. Find the point on the line y = ——223 + 3 that is closest to the origin. \ .2 A_ *9, .3: 2 inmwmws 5 5 2» 1:111 (“WW 6 3 *B _a_ ;z 5 5 ”MW ,1. : W4 W1, \zx +5? if f: it 5 fizwlgh‘xg’g C. ‘ 5 4 1 \ D ___ (m m.) < 6,3) 5» MC) 4% ++~+ 1mm 4» w w ,g E 3% E. 6 3 5‘ aggmrh \o ' r A ~~2(’<s+3~=iw13:43——» c1 1 mt)"; at M, ‘j E’l § 5 11. Find the area of the largest rectangle that can be inscribed in the ellipse :52 $12 2—5‘ + —9— — 1 A :2 >4 2.13 ‘ 4x “3 2, ? >3 4% A. 30 52‘ <‘ ” 53-1) B 15 - 2 U) ’25 {SSW-X7 0.12 — '3 <1 a -—-— 29 X S D 5 E {2W 5’ 2‘ at: 1 m l, 2.};- + «zip-x1 {m '1 Qgrgx I »W- , mm. m __._. ”MN—FAA 5 my W J S’ \las-W ‘ 1 ‘ 5 iv 2. TE 0 \n __ __ Q} éfl“ M + #7514 0y quAle. .5. 25:5 ch? in- S \FL D “Lair__v¥ an»? almsmcvx S“ E \FZ, MA 165 Exam 3 02 Fall 2011 Name: ..________ Page 8/8 (8 pts) 12. A cylindrical can (with both top and bottom lids) is to hold 2000cm3 of oil. Find the radius of the can that will minimize the cost of the metal to manufacture the can. Ar 50 C337“ vmflw A" 7? 5 5‘ A THE“ :QOGD N 10 cw» v A rim-m? Jr 9W“ *3 V? A : EWTZ" 211%“ $30 10 C. —- ficgfivl’l‘ 4000 7r _ . w 20 claw. 2: 477‘? A A000 D W dT“ , V” V 7W2. 3000 2 ¥ “5“" (2' E ‘9‘ V 77' Wdi} :0 m.» If}? 13949 CUP ’7’" W: iii-«- , . W t ‘ )0 1H '3 \G? ...
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