Sol-165E3-F2010

Sol-165E3-F2010 - MA 165 EXAM 3 mFall 2010 Page 1/4 NAME...

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Unformatted text preview: MA 165 EXAM 3 mFall 2010 Page 1/4 NAME @RQQWQ 7% Page 1 / 18 . 10—digit PUID Page 2 / 36 l P 3 16 RECITATION INSTRUCTOR age / Page 4 /30 I RECITATION TIME TOTAL /100 I DIRECTIONS 1. Write your name, 10—digit PUID, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3 and 4. 2. The test has four (4) pages, including this one. 3. Write your answers in the boxes provided 4. You must show suflicient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators or any electronic devices may be used on this exam. (9) 1. Find the absolute maximum and absolute minimum values of the function f = 2: 4 on the interval [0, 4]. a; ,. £2 x) ... {X37491 m M_ if x V, a l' l ‘5“? (07 45 ,7, j ' “a. “a ,K, X "‘ gr .6 £335 \ 4n v» mm m 4 Fix a me 192‘ g ram: 2 ) ‘ km g. L G v WWW w 4 W. 0 "mag; {:33} . $817 “3 O a”:m~valos. was. '2’: $22»- 2:63;: orbs, "imam, r «a abs.max.[f(a): is C?) ’ fl. abs. min. = 0 (33 J .v. he) 3:44; ":2 7;?“ (9) 2. Let f(a:) : 5 — 27% and note that f(—~1): f(1) = 4 (a) Can you apply Rolle’s theorem? circle one YES (SO) (b) If your answer is YES, find a numer c 6 (—1,1) such that f’(c) : 0. If your answer is NO, explain. g“ l , . i» .. g I???) 11‘“ fl 2;” “NW ‘5’: g (A neat aria {gaff/“60'sz 1 7‘ - O 9: g 9. Mr is?» 12 WC . (a it) Lil W? \m emf“ C/ MA 165 EXAM 3 Fall 2010 Name Page 2/4 (30) 3. Find each of the following as a real number7 +00, —00, or write DNE (does not exist). (a) hm 3:517. i153 3,4 m <5" mi.» Q {um 52 E; g; E‘fi’g az—>0 O {172 xfigo (23% my gram”) 2. N m 0 2 , EL, . «i , a; “’4 (b) lim (:0 6% ~ LW W(‘5 x mi) mvz‘m 00’ 3m 00 ' W) ' Q ,1w 34$ 1. A ‘ ‘3? ‘ :‘g LY“ gafgifliig 'w e w :2. @915 Xmfifio m (L m“ ymmfi 5H “2" (0) 11m 8m 52: m Efifigé “1:: ‘5” :1;——>0 tan {E WW0 r3 Sgcfix a W 4% 0 “a I+va , 1. ’smx—xiw . @gvywfi Lfir‘ ' .5 Emma” d) $136 3:3 “W” Wm’mwm m M" 62>? ‘ a ,x w 0 3%" 7WD \ fi % ~ w% g WW3 “A? 6 g I (e) 11111 (03051: — cot Qjm Jaw w é m—>0+ X “70+- 3%)}; «gab/“W / l :2. Kim wiwmmflbm I O I Wag-«0+ “‘“Wgfiw‘“'"” W Wm? caviar ~ V QM m”)? r 5 , E; m ' if (f) lim(1 — 333)3 “if Kim elemc'mfl; :7 €937} @éfifg??? "7' fl ., - .3 I 5 m ~ , 1% . 5W”, I“ 3) W W A m ’3 Jam :43 E‘ ‘ L333; WWW Q ‘x gm; 1 O ‘ 2‘ 2 5 (6) 4. If f’ is continuous, f(2) : 0 and f’(2) : 7, find W 0 a: A / Rim flaij‘féfig gm W40 “Rf _’ 9fwa 1 L M A; @)%WM%WM%TflW$#WWmflgvflA a 9’ E: £0.17“ +3?) in» SW A”: {2+SX) bewwbfi 3g.» / xi: *3 --/ H2») kifl ‘3? f {a} @ :37w§9$5€a 5% [Q MA 165 EXAM 3 Fall 2010 Name Page 3 / 4 (16) 5. Let f = a: — In :13. Give all the requested information and sketch the graph of the function on the axes below. Give both coordinates of the intercepts, local extrema and points of inflection, and give an equation for each asymptote. Write NONE Where appropriate. ‘ £09 :2 "x mm 2 ornfiiw is” Q 1 - :1er 17 MM ‘3 l a? , +— l l l”— | l > :13 ., [Jewryfié L :0 W gm 0 —2 —1 1 2 3 a was 7; ~ filmy / f“ WM —1 mm“ _2 ipfiemih W gjmw’va 1 New 4/ HA. [17m (xvii/aw) K domain i (0,9,5) I W x 4 at) ,' £me W as :: ' 6% i m imflr” ”’ . iijw {x ] intercepts No N E” t w 0 N E 0 5 symmetry ()N E (‘2: w firm i ‘3 m i N i I 7‘ “i 0: horizontal asymptotes l N 0 N E 5' (X) '3: "" W70 2”: l3 3» 72": vb vertical asymptotes 7c 2: O r a w 0 -r ‘in‘TMW w a l ' ’L . . , intervals of increase 00 m: min, (1) ) J i? (a) "3‘ ‘1' intervals of decrease ( o 1) I/ i J £ (70 "it? “9””; 3’“ ‘3 N 3 A?“ v N}, “7%?” local maxima O N E: l local minima (1 [Q I ) intervals of concave down N 06% E 1 intervals of concave up C0) 90/) } points of inflection N 0 N i; I [ n; I M MA 165 EXAM 3 Fall 2010 Name Page 4/4 (12) 6. Find the slope m of the line through the point (3, 5) that cuts the least area from the first quadrant. ‘ (69' 0} throw?!” (3)5) : fifigjm<x_3») WAG 1'0 W Cmfi; 6%; «yéjrnfm ~ 0, Nfi/ 43 #6“? L21 A '" W ; % émgrlwrvcm‘l’ W jtfisjt“ «Sm—25 N V j, »,3m) __ . 7 WW. . \\\ A w 3 (D “a :2 "m M A z 5.5” m «3m m W35; (’33 ) “’9 4 V” ‘0 ,ow'svzmz‘chm 52+; "'5 7—“ l j 9 ' §-3m_5‘ Mgmiv’r; 3.: V/ v m fly“ 2” Tm ROY"? 2mg Kl:j,.,/ ilfi cg 2§5w9m¢§0 .19 W133; w} m “it-Mg m _ m ml O . fl« WWW w / dili’fi‘ 7mm chm W :3 a (12) 7. Find the x—coordinate of the points on the ellipse 4372 + 3/2 2: 4 that are farthest from the point (1,0). 1 (6) 8. Find the function f such that f’ z {ifo mafia we 1 2: matte”) + <1 i t. “E 4% C: it???“ WV” 3’ m2+1 Xzbfi ‘: (é) Refill:- '\N Hm) : "thaw/Lag %’ 1 “’1’ 3% L is LWWE :9)“ijmtfmitfilifc‘hV7“? 41 MA 165 EXAM 3 Fall 2010 Name Page M4 (12) 6. Find the slope m of the line through the point (3, 5) that cuts the least area from the first quadrant. Let A EM 0; unit «3,25;ng M "ii ' Q MA ‘1'“0‘ ml: m %}\C)€VZ< is ? x‘ m, » m as A w ax kl; (me a {ml lam” “CY i Gun 3 y L “'3. , w a ab 9—> 3 3) w >03, m w» a: we“; a gfia A , __ Azéxefig EEGMW;@ Swexarm a»; » am ‘ ,, A- m y g, a"? ,, §,%:OI ,___7'”X::6 X53 la ‘ l m U“. Fox-mt» w w M ii?! 3 I 6 - ’f O, 5’” S: e l“? “ET”? " " E? abs mlw (12) 7. Find the x—coordinate of the points on the ellipse 4502 + 3/2 = 4 that are farthest from the point (1,0). (6) 8. Find the function f such that f’ = ...
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Sol-165E3-F2010 - MA 165 EXAM 3 mFall 2010 Page 1/4 NAME...

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