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Sol-161E3-F2010 - MA 161 EXAM 3 Fall 2010 Page 1/7 Name...

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Unformatted text preview: MA 161 EXAM 3 Fall 2010 Page 1/7 Name lO—digit PUID RECITATION Section Number and time Recitation Instructor Lecturer Instructions: 1. Fill in all the information requested above and on the scantron sheet. On the scantron sheet also fill in the little circles for your name, section number and PUID. 2. This booklet contains 12 problems, each worth 8 points (except problems 3,4,7 and 9 . are worth 9 points each). The maximum score is 100 points. The test booklet has 7 pages, including this one. 3. For each problem mark your answer on the scantron sheet and also circle it in this booklet. 4. Work only on the pages of this booklet. 5. Books, notes, calculators or any electronic devices are not to be used on this test. 6. At the end turn in your exam and scantron sheet to your recitation instructor. MA 161 EXAM 3 Fall 2010 Name ___________.___ Page 2/7 1) A tank has the shape of an inverted circular cone with radius 2 m and height 8 m. If water is poured into the tank at a rate of 4 m3 per minute, find the rate at which the water level is rising (in m per minute) when the water is 4 m deep. 0/139 §€,«L7l\<;\ {if lam/“ti ‘4 2, ? 7r ‘” him/N Gig-42': YE: ., a w Q NM ill le/xlngl'l/ mi ) (HT 37r .. k Q D)§ h :i 7T warm :"val E); :1: h m 21 3 WM 3(Ifl ls“ WV ggEMlEl/l’: .9) LES-E‘Wbé’k ‘34qu if It My up a 0/}, if; 2) Use a linear approximation to compute the approximate value of {78.06. '«I A) 2.04 2 .. Wt «PM? >4 a“ ?' B)2.02 ,\ m \ __2/3 C) .005 l M W Z 3‘ ~ D) 2.01 \ E) 2.0025 MA 161 EXAM 3 Fall 2010 Name —________ Page 3/7 3) If f (:13) = $3 + :1: —- 1 on the interval [0, 2], find a number (3 that satisfies the Mean Value Theorem. 5 C) _ 3 ¥Cll”%(QL , qQl(C) 044142, L‘fo D)? (7,32ka _., [ow-v1) 2 mi WWflW M w«« mm 2: 3C ’l‘ ‘ \/§ 1 L: 3: gamut | i 0 l 3 a,» i :1: C, 6 4) If m1 is the minimum Of f (93)=$3+3x2——9:c on [0,2] and 7712 is the maximum, find m1+mz. A)7 (ti cowlw‘nuous , [012:] K a (/0)ng Mew/bl. .4) . (3)5 \ . L ‘ l/m);3i téX'o) D)2 :3(%Lt2~>€’3l \/ {3—52 : 309*? W“ ) wax: 7%) 1 fig 2: 03+3ML’6‘M : 0 ‘ «C(Il : flgzafw‘em 3“"? ‘5‘” MAM.) “3(a) ‘7—‘1 2, WW (My) MA 161 EXAM 3 Fall 2010 Name ________________ Page 4/ 7 5) if f(a:) = sinh(lna:), calculate f’(2). «QAX "7%“ A) fol v? : Q " gm 8 (>4) 2 v 5 I B) Z _, ,_ 3 Z 5 @g PM 3 ‘ Jr 3L0” E); M (Z . l Q W»: “W :;:£ 2, 2 Q ‘l: 6) If f (,z“) = t2 + 4cost on (O, 271‘) find the interval(s) where the graph of f is concave upward. \ 7r 117r £(&\ :1 2%; wt} gm, “t A) (0’6 U<—6—,27r ‘\ 7r 571' 19(th 3" Z * 5L CW6“ " .(376‘3‘ g l 271‘ 47r NM Q0 v3 CDS’E‘ ”’7: C) ($3) ,3 3. 5, SJ; 7r 11w 3 I 3 D) (6:?) H QT‘ 71' 571' O LBL «95'» 2W E) (0, §)U(—,27r “WWW“W r {}> _ “T + ZrLl cost“ \ f 2F 9:: P megabafi MA 161 EXAM 3 Fall 2010 ~ Name____________.____ Page 5/7 A) 1 local max and 2 points of inflection B) 1 local max and 1 point of inflection C) 1 local min and 2 points of inflection D) 1 local min and 1 point of inflection @ 1 local min, 1 local max and 1 point of inflection / L PM “:0 ”a X ‘” ~21 \1/ C70 ‘90 1, ’2ij W 1 NJ 7< 8) Find the least distance between the hyperbola 932 — y2 = 1 and the point (4, 0). 7., v7? :2. 69X?" A)2 MA 161 EXAM 3 Fall 2010 Name ______________ Page 6/7 9 1. sinm — :1: _ ) $136 tanm —- a: _ 1 O _. “6)” A) 2 m7:: 'le ()5 X 5: we 2” B) _1 $014, x W l C) 0 Q 1 : “M fixim D) 5 7‘”) o flamsxmfi E) 1 o L flex/2’74 Wx 3’ [M /‘ (M x W x~> 0 _ _. J. 7 2. ((53.5; >4 Sfifizzfi A» 2 {flex Sac/)4 W X +3W\X) : :Jm :2, M .11 21 20 «km / O ' 1 5:1; __ 10) $133+ (1 _ 3m) I V9)“ A) 1 3A (1&3 M 7 B)e_15 I ‘(hm $916 MM @e_3/5 >601 / £1,171,“ D) 6—5/3 6 ) EX ”3/ E) e_1/15 1 \m 4, K ((«M 5. 1 1.}?2211_1_1,1,1,” ~ 3 E MA 161 EXAM 3 Fall 2010 Name ___.________ Page 7/7 11) Let f’(a:) = (:1: + l)(m — l)2(m ~ 2). f has A) no local maxima and 2 local minima B) 2 local maxima and no local minima C) 1 local maximum and 2 local minima D) 2 local maxima and 1 local minimum local maximum and 1 local minimum ll» [0C4]Z WW ,1 l lbwfl MM 12) The graph off’ is given below, a S a: S b. A) f has exactly 2 points of inflection and exactly 4 local extrema. B) f has exactly 2 points of inflection and exactly 3 local extrema; C) f has exactly 4 points of inflection and exactly 3 local extrema. f has exactly 3 points of inflection and exactly 4 local extrema. E) f has exactly 3 points of inflection and exactly 5 local extrema. Ll We WW [ W cal/W 4W1» 4 Katmai) / g PR. 34? luglflflfiw (evil‘ c' )CZV owl (:3 l (/ka {DELI/09W [\ch Wu? Mal deal/€43; ll?) ...
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