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exam2_sol - MA 174 EXAM II gm Name PUID Section SHOW ALL...

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Unformatted text preview: MA 174 EXAM II 04/01/2011 gm. Name: ___.___ PUID: ____._______ Section: SHOW ALL YOUR WORK. NO CALCULATORS, BOOKS, OR PAPERS ARE ALLOWED. Points awarded 1. (10 points) 2. (10 points) 3. (10 points) 4. (10 points) 5. (15 points) 6. (10 points) 7. (10 points) 8. (10 points) 9. (15 points) Total Points: wmmnwxwxww mm“;WWa“m“w.mm“mmWmmmmmwmwmwnwmwmmmwwmwmmmwmwyaw g 2 3: g ,3 1. (10 points) Find an equation for the tangent plane of the surface way + cos (my) —I— 'y — 2:2 = M2 at point (0, Z712, l). 3“”) $11: I:(X.j.‘?>) 3 9063+ 00M} “1“ 9 ‘"’EZ"/h 1 Ct) /,, T: : ng’ggvng ?X/( D; “511): Q, L, /hZSl/J-\O:; W B m: “* ‘ _ F3“ [X491 “XS X394" (/3)l\3xihl,)) : O‘b‘f‘lf/l W“? leuz J5 2(X/b)+ [(gllhz)~ 2(24): 0 D)”~ 2X+yv222 /n2/'L . . 8w . . 2. (10 pomts) Fmd (Eh, at pomt (x,y,z) = (0,1,7r) 1f w=m2+y2+22 and ysinz+zsinx=0. N. as ' 23L , ’7'- (ax )j , 2x+1i «DX 3‘?- ”- d 4-): (but. th‘9‘.$): \‘jgw‘fi'f 25L1><> ax ' —% zanx 8% 71,000 : __ ._ ’ :5 —--~ : " f flCJOi‘fJVix 2X (0,],7v) QD/(JjLShD Wmmv«mm»«amfim'safiwxiwWWWWWWWWWMYWfiWfiW mw‘:wmmm\mwmm . 3. (10 points) Use Taylor’s formula to find a quadratic approximation of flag, y) = 62“” at jaz(0’0)'7z«xg>z few w 4+ m + ~~;—<><vwwfw+mg 3Com: e5! fl 1 (QM/ti ; w, at No) x, {>043 @1221 j ‘4 L?” N 3 QWJ ;, ate.» 2X#j 4. (10 points) If the derivative of f (cc, y) at a point P in the direction of i + j is 3\/§ and in the direction of i — j is 2\/§, what is the gradient of f (:6, y) at the point P? .J a.) at fi/P : 0x6+£J ‘4 \J 'V .J Q ~. ' Z M a/:) Q (Ma/f” MW M )ldil 5. (15 points) Find all critical points of function f($,y) = 3:4 +y4 —— 4xy+1 and identify each as a local maximum, local minimum or saddle point. we ~~:> X 62- >< : O «‘5 wxflmxiocfiwm : lxc VX3~¢Y :0 ’5 y‘xs} l7< Wk“ ‘D “(My ~— scaa 7mm: ('1) 3X (~l,—~’) M IQUJ M/Uméllw. t t l E l g I; fa % t r 6. (10 points) Set up an iterated triple integral that gives the volume of the tetrahedron in the first ootant bounded by the coordinate planes and the plane passing through (1,0,0), (0,2,0) and (O, O, 3). Do NOT evaluate the integral. (3.343: 7a FUR/ML ?W5W (raw/ramyfi Imam Vi) éx+éy+22~26 l/vuz. g'L’W/J} (owe/WV c/l%0lyoix> éutxdy } 24mg ML 0 m1 711 g“ Wij/vjcme V3 éYflycé y 03/ 2304 7/1} /‘ y >/J )nvrl’) W o [M Z'Z-X /{ for the integral foz fag” f (m,y)dydm and write an equivalent integral with the order of integration reversed. SAX. w W % {7L1 Fajita; v5 Um X—Swwth, , chum w @7wa [It 9/ fwd/3 ’83 7541 JAN: 3:; LX) : X-lnml’B W D g J; Ye/J‘M‘h W 0 £2 2/ 8. (10 points) Evaluate 0’” OWermdy. 4§$Pc {£2 ffl;d.¢f./iéfivu}ué »5 tfi ovvh, Xfl4A7le th)n' \y n; ~c/q Pt 7Mwuw, L (fly/five w M U; (x 3‘10) “37$ {7% UM m? FHA/v com ci‘AQ/ti S . ”X: ymg 3*: rim/[‘19 akéflg 3 )’ MIMI/”(9 ZJ J‘f”lf{(’"”)"”em‘dw =3 f: f 52' '7»), l :J’: (aw-05% ”‘9 :(€~1/,,2-€ takes on the disc 9:2 + y2 S 1. SJ.- @ [Nb/RN p012}; {w (/10'4/Pcd pumh ’ZZX‘4’V :0 30 max / a» {X {Yczyabx :30 @ Awmj >51.qu M 2“ij 33(1—ry'"]:o I Cy Q}? :.,)\’;7_j 2\(+)’: 2/\¥ X b 2y+>(: 2/\7 QW-j)’; D ' Z 1 X*)’ 1} b<~3‘>CzM 2w 0%” 9“» a x23: 1 3% «fiyi! 6 _. cm} A“; “33*" 3:5 ><:-f)=+% ® dwk cu wank 736%) X"‘/ > "' i 3 _ (O v)“:D X:l~ii{:):’+-:_ ix:_, 63:93) I. [—4 : i if Art/413% 2’ 7“ maxf 7 D Z 2/ ...
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