# sols_mt1 - 2322A » Midterm I w 1. (10 marks) Find and...

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Unformatted text preview: 2322A » Midterm I w 1. (10 marks) Find and Classify all critical paints of the fui’mtian fix» : 173 v “i‘ 333 ‘” *3 "i i, is 2 ii} M £15 3 §€j§ 3 (“Him {>134 f3 ﬁx “3) A /M [email protected] (12%: “W: 5 my W E it; {Qﬁw)/§Z§§€<U}€ MAT 23224 ~ A/Iidterm I 2. (10 marks) Let 2: : fig: y} r: 63%? sin 1:}; 8: E331, 8,:- emd ~7— (33: If :5 a ﬂu v) 2 ‘21: — 3:: mad y : yfav is?) x :22 + ma (:mnputo both Chain Rule. using the I a; 4‘23 , “"s, {‘3’ A M \ GEE £25 7 £55 if" £53; @xil‘ia 3(‘3 a?“ 3&1} ff??? 5{ 3”)?“ ’ . 9» " {if is: W ,3 i: 3 {mi N w gEEQL 3&1ij a} ﬁzz/fﬂxﬁwfiéir’f Mwﬁ} 4” g {35: 5 (“if 4Q?)a Cy‘v [[2:3“w3a}(y2+éiw)> A “*1 ‘ Efiesmﬁai) Hie a“; 2. 7i” 5}” (2(ng 34% K?‘¥v”“35<)faf¥§5<wj +~ 3(3égwiéx}%{§gfi{iffz [95,? WEEK) 6 if“ g; 2’ ,gy’iw (y;%£{g?}€3{3 Egajﬁz‘w'ééi’) f 352 85%} “H i? if“ £5 3’3"}: f~ g {31% { [email protected](/U ‘ngjﬁg \ 2 i . ,3, a 36%“?aﬁé‘z9éiz333, . (iii? 352,326} £43} M3£€§f§€jé a?) 2 3‘ mm ,‘x I i E, A/IAT 2322A — Midterm I 2. (10 marks) Let 3 : ﬂit, : €63?” 25in my (9: 8:: a“ and using the Chain Rule. Your ﬁnal answers should be functimls of u and 22 alone. :33 If 11’ : My“? :} z ‘ ’3“ and y : 9W, = 27 + m}, compute both giﬁfwzi " is; ’3‘, m,» m 1542? X? db, % 553x {2352: cz‘ 3 “Em” , 19?». 332% 6:“ 55% 36% ff”? w 6 kg“)? 53;; a; :22; \$13 ; 3: {g ya. 3%) i~ {3% iii?" 1 {tan/2%" ” §é{3(z?‘%é€é?ﬁ)> i 3(Q’Eszgzg} ﬁféég‘g? (ﬁggﬁyw §é{}§§%ﬁ\$§¢:% (’53 2%“ éi’éjééﬁ’f‘ég :3}; (ngégé)? f i +9” éiéé'iféié‘g} \$ \$53 {:3 £333 ~ Aﬁdterm I :1 3. (10 marks) Find the global maximum and the global minimum of the fln’lctiou 2 x 1:3 + ‘29; on the Set. 51:2 + ye S NOTE: For part of the soluticuilg you are required to use the method of Lagrange multipliers. r w M WM if igﬂggg-é 5; gﬁ; ’iiégg ﬁgmgggzg MAT 2322A — A/Tidterm I C)! 4. (10 marks) Compute the following double integral // (2:4 + 33523;?) {if} R Where R is the rectangle 0 ﬁ x g 1, 0 g y g ‘2. E 2 MAT 2322A — Aﬁdterm I to 1. (10 marks) Find and 01215313 all critical points of the function f“ r if \$4 : W 2.: 5:M<: 22 ,, '“ﬁWﬂ ‘ f”??? {fﬁjgws iingé W “ MAT 2322A — Aﬁdterm I 2. (10 marks) Lat 59: 6: If 3? : 37(21, :2 42:, m 33 and y : Mu, x u + my (itomputo both { and w usin the Ch: 81? g Chain Rule. Your ﬁnal answers Shoukl be furnittiurls of u and 8 211mm. iaﬁig : #(“e éiiiéif f=~%(é€%»\$i\$”} gm {gssw égﬂféﬂﬁw) 7;” é \ (ﬁégg> € (fay Ea?“ f~3€égv féfiﬁ‘) Cg? (,(.%{« 33:){% WE C?{)\ geﬂég if} (:HW‘BQQR{[yag~§§3)fi{féézé})“IL” Em «- 5 \$35545 gag: 1;} i 4 e % axis» aiwm‘) , _ . g ”§E€ "3.3 {6‘ it y‘%((zgé{»§§)(éwaw}>+ a: E: MAT 2322A ~ Alidterm I 3. (10 marks) Find the globéﬂ maximum and the global 11111111111111: of the functkm flax y} K + 0n the get 2 2 M; S 4. NOTE: For part of the solution, you are required to use the method of Lagrangeﬁ multipliers. 3.? 5 ﬂ ,, ’ r? 1% ﬁg, 1 g 5;} is: a; “7% wig Wﬁwﬂ‘v 5‘” :2 {3:9} wégwiﬁ 3M may Eaﬁégﬁ W & { ﬂue y; 43 sag} ewé wag, W ,1, a? 'g ‘ MW/s MW w “a; 7‘” ‘2‘)” 3 ‘ le 52%;" ’5 ‘W’ l gzzwé~az>azaz *QﬁAﬁfi 32’»: WE é»g-2;;>bza{52; «3% >223 6’ W : “:9; 525:} “33) X “if ‘3} )(2‘: £2, MJ{/~ESG2§ WW : \$3 {\$52}f%2{Q§w?j M991: {£36 a, (\$.71 MAT 2322A — Midterm I 4. (10 marks) Compute the fiﬂiowing doubkz integral // + 3372312} 5: Where R the rectangle 0 g <3 TL 0 g y :g ‘2. ...
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## This note was uploaded on 11/23/2011 for the course MATH mat2322 taught by Professor Rida during the Spring '11 term at University of Ottawa.

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sols_mt1 - 2322A » Midterm I w 1. (10 marks) Find and...

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