mid2_practice_sol

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

This preview shows pages 1–8. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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»! ' \ ...
View Full Document

This note was uploaded on 02/07/2012 for the course MATH 1271 taught by Professor Ming during the Fall '08 term at Minnesota.

Page1 / 8

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

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online