finalsols - We: u 1. Evaluate the following limits. (1...

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Unformatted text preview: We: u 1. Evaluate the following limits. (1 point each). l, sin3t9 km {l" 36 KIQ COS Y9 ' 2 1 ; game-940 39 sme y L/ a, x \‘x k l/ \ ( l . LI 332—1 . hm (iv/00ml) r, hm ‘ 3:qu x—l x31 x~| x— t < ) 2 _ ac — 1 l' 11m = “"1. z—r1+ (a: — 1)2 >0“ . 1. 11m —smz= z——+oo.’,L‘ \fx+h———\/—z—1_ mm W , h ‘ 2. (5"!)[Y'l — I’m '2. —— :00 (/70 LY SiMPEZ—e (g Q i X 5}” K W44]?! —”l_?0 (’7 \lxrA-l +J7Q »<+A~( —-(s<-'!) a um i r “ hat.) Uxmq'fl/KT? a lim h—>0 a (ll/V) f M L‘—)0 L,(.l)¢h~l +t/K’!) am 2. Use the definition of the derivative to find f’ if f = 32:2 + 2x. (5 points). Hm gym-H'iEL) 2 lino 3(X1—hr1—2(xrh) ~3yZ—2x ln‘m in H90 k (1m CXk+351+2A [m logo A :L,(~>o (6x1'3L‘f2) : éxfz. 3x+1 a3<1 3. Find a, I) such that f = (1102 + b 1 S a: S 2 is continuous. (5 points). 6 — x3 2 < a: "M snow, if} wab = F“)- Y“?!- Ifm X~> ' 9'64): 4. \ ; 2 “a 5 ’93-), 5:3; m: —2_ 7?) 5% cpnfil flue/yflu‘fl) on each h‘ne abut/e WW5" be eciuqu (—(:q+5 -2,:L‘a+b \UQ Subf/oc‘l' 4. Find the point(s) on the graph of f = m2 + 1 Where the tangent line passes through (2,4). (7 points). ¥‘(X): 1% / 50 “>de7 )3»! (i'flc’j wukrm bevwepn ( X/ x1+\) Omci (21W), S/a/DE 2K / ‘1‘ 9 ZXiLJLLL 1‘)‘ 3 or 5. Find the equation of the normal line (line perpendicular to the tangent) to $312 + 2y - a: : 2 at (1,1). (6 points). d ,. “witty”? ‘i-Z—I '0 {3&7 M ((,I.)3 d d 2 “I 1- +2 .1... 3 z) C(Y / M I o TX :0 So fat/96"} hm; is Lori ganfd/ So flo/flmi line is ire/Hm (‘ TMQ Jeff/CG] “HQ Pc5Sir7 (ill) X:( K (73’ would 69 Molizonmklj . y 6. Find the following derivatives. (2 points each). Dx[a:sin(2x2+1)]= X cos(2x2+i) + Si/l(-Z)<Li~l) Dm [cos(sin(x))] = ~5 n (5; a X) C0 '3 X D [ 300w ]_ (44 SM ><~*) (‘35MX) ‘ 71a)st I (WEAK—{)1 4sinw — 1 7. A particle is at position s(t) = t3 — 22—1t2 + 3015+ 12 at time t. It momentarily comes to rest twice, Find its acceleration at each such time. (6 points). v (6): 5m: 36 ~24t + 30 =3(€~— 7t+/0)=3(t“2)(£~s‘) Comes +0 r951” whet“ i=2 or {25‘ C((fi): S”(€> 26f. ‘2‘ 8. Use differentials / tangent line approximations to estimate \/ 121.1. (6 points). Let y : J;— “Gaeid Pro" ((21, 1:) ~ clv _ .L ’ Eli ____ __l‘ E; ” 2‘}; dx “m N 21 flqh line :‘l(x-(2() 9. 10. Water is being poured into a cone of height 12 inches and diameter 6 inches at a rate of 10 in3 per minute, but the cone also leaks water at 2 in3 per minute. How quickly is the water depth increasing when the water depth is 5 inches? (7 points). 3 3 What is the largest area of a rectangle with two corners on the :c-axis inscribed inside the parabola y = 16 — x2? (6 points). D 3 Co, q j x2 11. For = m2+2, down, has inflection points, critical points, local min, local max, asymptotes. State any symmetry of H. Sketch its graph. (11 points). find where H is increasing, decreasing, concave up, concave We: 2mm ' 1*} 2* m-: A ($4 +1-)2~ {Walk I H ()0 >0 whom ><>0 ma: (0,“) H’m <0 mm Mo decr (-“°(°) ,—>o~ (’x‘)-co 6’ 50 Y3( '(s q Lodz} zomr —~ W (531-2) HUM 1% {9 ; XY+HX1+LQ~§XL1~MK1 ’ :“XWZW ., \ Y __, 1 r. ‘” v?» (3 1+9 1v {X l “ 1)q (leerl >( x H//(><l30 => Xi; Hybmx ~“(tS’ A 3 6 R g 3 “"3 12. Suppose that if a business sells :3 units of squash, it has revenue $4 + 4x2 and total costs of x4 + $53. How many units should the business produce to maximize profit and What is the maximum profit? (10 points). 3 X P: Proer :— Reumue“ C0“ 2 lez” ‘3' D: [0100) Filx): gx ~><2 :0 =7 XlS’K)=O =>X10 or x= FII(K) : 8 ’2X/ Fl/(O): ? >0 I 5'0 O ’P”(8>=-sz<o Wé‘o W ,x‘qulos may % (SW? M CWWM “Wild/"r5 NEW—25o 53%? 1:11, PM: ~09) l-e The busing» manual sell 8 qnl'rs (w 67“ Q MK mefink d; 1:55 7 13. Evaluate the following antiderivatives. (5 points each). 3 /(x2+cosx)dx= 2—; +54% Xf‘C, facsin3(5a:2+1)cos(5m2+1)d$= (7'6 Sngxafll “LC, Le} Q: glow—KIM) do : fix Cd${§><l*~‘)d>< )9 ‘2 X<OS(9X “ldx: % du § I , l I? g 0 {X 9”“ng F‘>C05(5x Hid“ : éiuiclq :LTlOCAL/f—C l L : 95 §inl(§><z+()7¢(f 14. Use the Mean Value Theorem (MVT) to Show that f = 51:3 + x + 7 has exactly one real root. (Hint: Try showing that it has at least one and then showing that it has no more than one). (10 points). 70,; (pm, am, 9 NW“ ma fur (rm as my: 63/1 0,47 1h berm, )K/w‘e fl-w) <0, $00) > 0 So“ £97 TI 3N ‘(“(0,(O) 5.t~ :O. rIf we and” warm" ropich Mumbws, coach Say (I'm x—am 79M 2 ~60 , 50 70 MWMW <0 1} Kflmoo : Q>0 5'0 @aowf’aaflr >0 M ‘0 r wk and P/OC9€C( Q5 aka/Q w’lbovgk Var/1M7 abbot w? ‘ ' ' 2 pm 0 a /; Q XQCHy 'p .3" 130$ 1L / {1070 we ‘4 7’0! (45 10 Am; a 7L /eas+ a n e [cad ‘ MOM 10m mmwv mics xt Min hm‘h) Le 9593” REFO‘ I m Mm, 31¢eron 5+ flcr—M 50 ymza (BL/(Jr $‘(C52 3C1 +( is never 26/0 (Wu'n Uq/ug ,‘5 (I) go 1mg "(3 ;mfoss§~‘>“°~ Th“) 30 C(oc‘s “07‘ have MO/e fact” one rec-1+. .-‘ fl [4&5 €><0£Cf(\/ cane mgof‘ ...
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This note was uploaded on 07/17/2008 for the course MATH 151 taught by Professor Any during the Summer '08 term at Ohio State.

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finalsols - We: u 1. Evaluate the following limits. (1...

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