mid2_practice_sol

mid2_practice_sol - Problem 1(20 puintsl Difll‘rvm‘imv...

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Unformatted text preview: Problem 1. (20 puintsl Difll‘rvm‘imv the function. (ill [5 points] f(.r) = \/'l 4 VT; '04 ma’ (70:): 7- HJ Hr? l \ l = - - CHRW NHJHW ZJHE: - ' I | ("J [5 p0ints] f(.z-) : L;111“(1u(siu.r)) / \ {’(xv = - (LIME-1 mo) 7 I ‘+ (LUme ’ (>ng = 2. ‘ —-—.-‘" 1+ (QAGMkW gmx ("3 [5 [mints] .HJ‘) = (cm :1'.)"”"“" 605 Le',‘ K3 _—_ (Cos 6095‘ P fixvzq':(cogx\ (—gl'wyfmkasfl —<m>¢> l-r + 1)(J-+ 2)3(.-r — 3)" l‘. P ‘ t; _. : ___—__ It [a pom s] .H H (I + “l” _ 5),,” +6)“ kejf ‘3: (:00, 9mg: JNCHH+2lbatu+13+3Mms)-4Ln(x++fl —;J~(Y+s\-6AM(H6) ‘3' ' 1. ‘5 1- _S 6 ""-+—+_"— x45 x+g .- 3 X-H m X4} X4“- (1+1\C'z-u)l0fi1)3 (4+ 1 + _}_ __‘__ -2. _ ‘— _ __——_———-——_ ._.—_ — (ac—mufflfl‘ (7H5? I {KAN-o I»; Problem 2. [10 points] Find dy/dm. (u) [5 points] 2-311“: 17 + 1/ +1 DidevW-k «:Jre bow side; (4, J. + Y Ma “(253+ 13.241 $1 = (W , AL; (2,8914ng t 'z 3 l‘zx‘fl vhf-l 3 \— 2333 cm _ elk " (h) [5 points] (0053:)” = (cosy/V Take £03 A be“ 8149:, LwQ/osflkg = JQ/‘~(C‘°““3\X ‘VJ = '1 ,. -S'HAV éfl -gmy _ _ 3‘12 )[Muosfl + b) TAX * kasLfl+ 7 0.953 «(V elk (“(Cosfl —+X‘bw‘3\%—3 : 0"(w’fi\+ ‘OW¥ Mum Jr a W“ cm _ ____——————---~-—-*" ’8'; " £46»chij Problem 3. [10 points] A firm light is mmmun] m the mp 01' u 20-ft-tall pole. A man 6 ft tall walks away from rlu- pniv wilh n ipoml of .-‘. [I s Mung :1 straight path. Ar what rate is the laugh of his shadow increasing when he is 3“ H Hum {111‘ pult" Problem 4. [10 points] Estimate \7 16.001 using a linear approxinmtion. fix» 2 ’(m (740* {cm I 'l r A/ _ __ 9 __ 1.... \(K)~ q X l l | me): = —3 =33 (n H: Problem 5. [10 points] Find tlw absolute minimum and the almolute maximum of the following function: my 18 — x2 for —2 5 1' S 4. LM (cm: 'Xlevx” 1 €00 = 13-3% +>L~ ————— fax) '2 m—x’“ H "(P I 1Q :3 vxz 43’ U ['8 -)<"' :1 q- 12) 2 (240 (2+x) V ‘3 'X‘ \/ I?-X” Ch“ng uaflues ‘. '3.-3 _g {g “A 1% HM doma’m. H (I 6 Problem 6. [20 points] Let 1 f(.r) = J?“ — 4:17" — 6. (n) [7 points] Find where f is 'uncrcnshig' and where f is decreasing. (h) [7 points] Find where f is concave upward and where f is concave dowmvx-ml. Find rhv inHm-Iiuu puinm. (c) [6 points] Using the information from parts (a) and (b), skvu'h the graph of f. 3 2 , '2 x- (co (m: 4x 4W - 4M 9 (’(r];o a" Y“: o , '3 1+ X<° . {'(v') <0 =9 decveasiwg fl o< ><<3, PM)” =9 u I( 30; (’00 >0 =3 Fucvem37n§ (3,”) {Kay 7fi>33 C—oa .7>\ (“V 1‘33 C Kc, Kncvmsiug av (‘ Ts decvmgc‘mfi 3% (L) Woo: \zx‘aw: “(W23 900:0 ‘3 X: ° '7' n -d DC 5((0 I (7)029 :4.) ('o (we U.\0l»0 I; o<x<1l {7(K)<O : =3 Conroy! quOd (on (awe lawnwad Li X >1 , 9’00 )0 (o,‘€(a)) : (°"'6) Tn-Cipdu'v poi Ms (2.. Q1)» 2 1.22) 3 _ 73 - ‘ (C) ' 4'0,” 3"“3 ’4‘ '3 6‘ ’fis Pruhlcm 7. [10 points] Slmw tlmt RENT > 1' for 0 < :1: < 7r/2. 9mm 99cX“ 1x>l {’oo>o ‘Fvv 0<Y“{". 90' .Q is [V‘CVQD\S|V\% ah {(0)1't0w‘0'0 = m. «mo +5» bowl;— <= th—X>o (‘4) JCAMY>>¢ Problem 8. [10 points] Find the limit. '1 e" — c" (a) [5 points] 12 _ 4 : fiTtv‘ e Y~>Z 2X \l e2. 4. H (h) [5 points] 11111 wlu(sinm) x—O" 4 J. Xflo x 0/05" :‘ JIM fiw’ + I H -.X_L — .wa —xzaw 3090+ (My ‘ ,w -'2ycos><+x7'9?v~ ‘ ( 0+0 H [I O 9 4‘ 1+9 «be Past r .2. ._ {‘04: $7M»! ' \ ...
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This note was uploaded on 02/07/2012 for the course MATH 1271 taught by Professor Ming during the Fall '08 term at Minnesota.

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mid2_practice_sol - Problem 1(20 puintsl Difll‘rvm‘imv...

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