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exam2_sol

# 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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