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Sol-161FE-F2009 - /4(a/~ FMQflKJ¢~ F/M/LL EXAM grflaffi...

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Unformatted text preview: ///4/(a/~ FMQflKJ¢~ F/M/LL EXAM grflaffi m (1) The domain of the function f (cc) = x/1n(a: + 5) is: (a) [0,00) A (x+§> 7/0 (b) [~5,oo) W»; 8 Raw) 3) 6,.0 (C) [5,00) . /> X +9 ‘7/ ‘ @ [—4, 00) «5 NEW “‘3 H, 00,) ' (e) [4, 00) (2) Let f (3;) = \3/ 2 -— 3. Which of the following is f “(13)? (a) (2—3:)3 Tfiech/kawga O< 07ml 3..., (kc/1f: 1am) 3 m2+9 form<1 31f a: = “‘ () fl) 12m—aw2 forw>1 uous at all values of :13. , JAM—— ‘ngXl 2:: AV: XL+QS -: ‘0 determine all values of a so that f (9:) is contin— (a’)a:0 del X’Bl (b)a=1 @l’ fig”)? £T+ DX'QXZ: [2% Md W ' fig 1 ‘ (d)a==3 X9{ ‘0”) 7498?”? PM; ‘3 \D [7, a (6) There are no such values of a (4) If f (:13) = 9:2 teams, the slope of the tangent line at (g, f (3%)) is: >247r +6\/—7r €2V§Wg +2\/§7r 9 .24: (d)? 3 (f %:3 2‘1) (WWW: :3 lg 41”? 3 M Q A @331? + LlTTZ (5) If “90) = 64”, evaluate lim W h—ro h (a) 812 (b) 6" A; lZv—ka 1L . j e ‘_ r I : W e 7" 6W4) 1mm; 7 hwwm £2 IL LP LA :3 /é4m C ,% MM) 1 lL 40,4 9 a i W; L \‘L 332+1 (7) The function f(a: )= $3 +8 has ' \fefilfii} 4224b W’Mfi (a) no vertical or horizontal asymptotes X3 at“ g” WE} ”=5 X 3 W27 .1 vertical and 1 horizontal asymptote W5 5% Kiri filigj 4M W‘Wfifilfi / X “” w . (c) 2 vertical and 1 horizontal asymptote (d) 1 vertical and 2 horizontal asymptotes l (e) 1 vertical and no horizontal asymptotes $00 X3 .Hg 0 (8) A particle moves on a line with velocity 21(t) = 13—1110?2 + 1) What is its maximum velocity on the interval 0 < t < 2? (a) 1~1n2 u __ v 24;; 3215 H =L‘) (b) 0 v M P l 152+, t tit '57 H l . @2—1115 V (6)94) “.3 (6:! (d) 1n2~1 nflwgmmflmfl W \f‘zél “€79 defetrma‘me, {Del/thwart“? \f‘ we W Mme «be: «ELH M£fim \/ ‘ig threat? 0% 63:23 68le wife) 4;: WM Welling“ (9) Assume that f and g are differentiable functions defined on (—00, co), f(0) = 5,1703) = 10,f(2) = 5,f’(2) = 4,9(0) = 2, and 9'(0) = 3- Let WC) == f(g($))- VX3313”)? Wm 11 Pgm) ~ 7%) <b>8 W0) 1 New) @ e‘fa) (c)10 3 ”(:‘(fl 3 .12 '3 bf * ‘3 (e) 30 ' :3; if; (10) Assume that y is defined implicitly as a differentiable function 01°53 by the equation 2:23 + 32%; —— mya = 2. Find % at (1,1). .7 5?; we; m we (WW) We. 5&ng /fi3(gf) eg’flgfdfifl a :o ‘0’” M“) Q? H“ + iii-”4+3” e _ a e_ we» /2 3: gm “4 Ge 7 cos(2:c) »« 1 1294 Q 11 Eval te 1i ( ) ua m (:9 {3 @_2 {Is—>0 <b>—1 ii fie 494%). ( KWZE {:3 ix 0 0 ) 55” w M ‘ (d) 1 :2. )graeo Z ' I <e> 2 _.. we. — 2m (12) Water is withdrawn at the constant rate of 2 ft;3 / min from a cone-shaped reservoir - which has its vertex down. The diameter of the top of the’tank measures 4 feet and the height of the tank is 8 feet . Howfast is the water level falling when the depth of the water in the reservoir is 2 feet? (Recall that the volume of a cone of height h and radius 7" is V = grzh). 2’ o . é! :, W E (a) gift/mm WEE "ml 'E km N ' AA“ 2, m E (b) Sft/Imn ””1 3 (Vfiwcme4, JMELwEm/tj E .. E (age/nun 4" WW: Efi—EEUJM ha' 8 WV mgwgefim (d) gft/nun w A A .2; 16 Q h (e) }— ft/mln T Z .L $Lh2‘_l3wol\/w:[1~éiy WM 3U) h “” 49“ > if} " Lt“ OLE hm“ w, :5: Léh étm E49 ,9 f i e, M W Z {A m w W m \ 2’” ‘5 6“” My? Aj" (ZYW' ”I”? (18) At the beginning of an experiment a colony has N bacteria. Two hours later it has 4N bacteria How many hours, measured from the beginning, does it take for the colony to have lON bacteria? (>ln5N W) W0) 61% (W0)$ N a 1112 k1 ’/ We <b>§1§ We 1 :2 W 11 6 a: (c) E; 1.11 1% 25'? :n f:1WW (d) 4% flwflgxa P—flrwm P (£\:M;[ €w>fi 1112 % £1 {I Ate ‘11 fl 3; ”Ag“? ” :1 {fig—(’9— [LAM 13’" £4 1 (14) The apprOximate value of (16. 32)4 given by linear approximation is equal to .2111 1:)?” «9(743'” xtf 6014 Ram) (b) 2-10 34M +§at )[Kmlefl (C) 2.02 LWEVM ‘3 it? 7: 4‘ . W044 W Fag Q (d) 2.20 A ,1. (e) 2.06 MM 7;" Z 4‘“ g2, (W49) 2/? - (15) Find the critical numbers of f (x) = 6m sina: for O S a: S 27r. <a)7r/4and57r/4 ‘ QM; efgimwk» €9ch @37r/4 mam/4 : Qw'gfim ”FCQSK) (c) ”/4 and 37r/4 (@qu 3%“ {w Mi mmigwg“ >1. (d) 7r/4and77r/4 96% :0 W3 gmM—rmx W “W5 S(\/\‘/\ =1 ”0357‘ “‘2? flix fr» _.\ (“03%, ’3’ W74 :4 yx “9 X t: J mg 7.32: l l / ‘i _ Pt I Q ‘4 1 _,, L1” V2,, ”V“; (16) Compute/1(f—fi) dx ,— f (X ”RX 34%, (a)2\/2'—10/3 (b)\/§—1/3 . ‘6, 0 fi 43 3/» ‘17.. 3 7/3, , <> +/ .3 EM ”My/(fl 2: (d) ‘2\/§ + 14/3 \ 1 .8/3 : 2.6.»gMZvZ ”(“3"“33 (a E : Ljfofg—FZ *2» ELL... 3 2. _ t E; , Jim? 10 2m (1'?) Evaluate ii— (/ arctant dt) at a: = ; dm 0 :1: 71M3 f:{£: HAW {” 491’ ) “1: QM?“ 35(1) (0) 7T/4 , m ‘ .w/Z ‘ 63% X’s” 17: ~“5 (\ng !>[L) —: a!) (L) 1:: (e) 2 ' (18) A certain function f(:c) satisfies f”(:2:) 2 2 — 3w. We also know that f’(0) = —1 and f(0) = 1. Compute f (2) u m .—1 wfl [fl ”Z-W (b) ~3 ,5 PM 2': 2W“ €34” H; (0)3 pm 7.: W1 3:. 6 ~O w-§ Cl-“:‘:»m( (d)l ' Z- (M "5 M): 2w- éx a 00 11 (19) Compute lim(l —« 9;)? : ‘ 57% m—ro (d) 6‘3 g/ (W ‘29?“ filfla) fl :7 g; ’i’fi/{mfl e e __y r w W: We e: M (20) The derivative of a function f is given by f’(:z:) = (an -~ 1)2(m — 2)3(a; — 3). Which / of the following are correct? 1 I) f(2) is a local magdmum and f(3) is a local minimum of f(93) I: II) f (m) is increasing on the interval (1,3). l ? III) f (11:) is decreasing on (—00, 1) and increasing on (1, oo). ' @0111)? I is correct V :00 (b n1 IandIII eor t MM ) 0 3’ ar C rec ‘ {@133 (0) Only II is correct )9”; \ . (d) only II and III are correct ”(L /7§l (e) Only III is correct 4 12 L 2 %+%a @wl all: Q’H‘)‘ (21) A rectangle is centered at the origin, its sides are parallel to the axes and all of its vertices lie on the curve 4m2+y2 = 8. What is the maximum area of such rectangle? J'QJJHK‘“) \ 13 (23) On What intervals is the graph of f (ac) = :04 +4003 — 18$2 ~— 63; concave downward? 3 l '3 1 (a) on (~3,1) and(2,3) Fl, A4) 2% LlX whng dgéxflb (b) on (—00, ~3) and (1,00) (0) only on (—00, 11) (d) only on (3, oo) @ on (-3, 1) '(24) The figure below illustrates the graph of the derivative of a differentiable func— tion f which is defined in (—4, 4). We can conclude that f (:13) achieves local maxima and minima at the following points: ‘local maxima at -—3 and 2 and local minima at ——1 and 3 - (b) local maxima at ——1 and 3 and local minima at —3 and 2 (c) local maxima at -—1 and 3 and local minimum at 2 (d) 10Ce1 maxima. at ——3 and 2 and local minimum at —1 (e) local maximum at a point between —3 and —1 and a local minimum at 0. '14 25 The graph of the function f so = «1503 — 111:2 + 230 + 2 looks mostly like 3 2 “’39 M3 06%? 6‘» Q95 kw (mm MA MAM Fgfivfifi Lbcaj‘d 0‘1” H5966 (yaw—wwm a ...
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