Wk6_Solutions - Worksheet 6: Prelim II Review 1) Estimate...

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Unformatted text preview: Worksheet 6: Prelim II Review 1) Estimate how much the value of f(x,y,z) = ysinx + 2yz will change if point P(X,y,z) moves 0.1 unit from Po(0,1,0) straight toward P1(2,2,-2). V79: 476(08):, s'h‘x 4.2%: :B Idfiflav> 2~~4= “3:. 3 l a» ~q \r Ci; ( What is an isosurface? Pick an isosurface for f(x,y,z) above and determine the tangent plane to the isosurface at pt P1 . Jan-apt 5”” flaw}: C— "0 {(2-,2.'2):-1’2"“"1 “gwa Ago/Mg; M p7 . i u r 4. , VH — a - . in . “La—2‘)“ 199:2, slin'z‘q H > . ywmcfi‘wwk‘: ( / 2:052< Y”Z) “If (S‘nz‘ L) '5 Vfl‘l'fiw (5+ 4 , as 2) Find the linearizatron of g(x 3,2 W) at the .11 pt P(1,u,1,1). g(x,y,z,w)=x2yz+ey +w2z %(K”\/(%lw‘>: «3" i} +iiOX r if; fly A”: GL9 V M x ,2? oh.) YE; 03‘ + K E+é_ 1 ’3 + x +w7‘ 51 + Zwl ‘P x i? y L K/ p = Z + (2+ e') o\/ +- 0% + 215w - u 3) What is Fubini’s theorem? Ore)er on; \‘A'H'a IG‘E’l'fim “‘4 ‘g’m‘w‘g‘4’rhgwi Sh S‘Tm \ 3 M f" h {M “U; l C) 76 “a m 1‘“ E I if; ‘é. 9 30“ v‘c' 3mg); 7’: Y 4) Draw the region of integration and evaluate: ‘1 rah/H2 I J [1n<x2 +y2 +1>+xyidxdy —1__h_yl “W (L'f {rt W \ f E (lv‘ (Hui-l) + (“wag minim) O ‘3 I L M": rk~v( a in.“ ?w e} r ’ iri (1 \ u a l in? Zun- ( A) \ + I“ L05 ’ fir-rag é Worksheet 6: Prelim II Review 5) You are an engineer at a manufacturing plant making rubber duckies. The cost of making rubber duckies is CH, p, s) = l (p + s) where l is labor time, p is cost of parts, and s is the skill level of the workers. Due to a union agreement the labor is constrained by the skill level as follows: I2 + .92 =1 . Due to a supplier contract and “just in time manufacturing” philosophy at your company the parts and labor are inversely related lp =1 . Assuming you have complete control over labor, parts, and skill level of employees, minimize the cost of making rubber duckies. 6) Setup the integral in rectangular, cylindrical, and spherical coordinates for the integral of f(x, y,z) = 6 + 4y over the region in the first octant bounded by the cone 2 Z = lez + y2 , the cylinder x2 + y2 =1, and the coordinate planes. I ,. x1 ‘f‘ XZ+Y2: 3 9. a ’ a g Q+lei cgéeléydim :7) J (a .r Jame” x ‘ 3 g g (IQ-r-LFCFSerJXJ) rc}r‘c§@ / D O p =(eugf r 7’7"?” “71 / (Jag “p n g g” E (to 4-“10: sunflnusefl 331‘ stf &P C) “hi 0 L 7) Determine the flux F= <x2 , y2> across the closed path r = < cos(t),4 sin(t) > where OStSZfl. v: 4:..awxéi‘iwtb‘) 3“" a T“ x 12 ‘1. .t » , semi at. - v ‘5"? :4. J" [M n 7» ‘ ) u v"; ~ \‘ .r ,m. i d" __ r l”, auflatfla '1 / f T: Z- H vs t S ‘.At‘>( 0 ‘ “ Muff ,, . pr WI film”; *léwmfié 3:) L! “53-6, + '(a 3M3 t: cit L (“ZR I, 1 g‘ a 5” Lt. .- ) J 5 1r;- .\ 1.17 '30 Lus‘t Ll -SIV\ fixcj't-i-HOX glntl( hififméscf {3 2;" HESM'C " ink-x 1. {biedmfi «(- gustn/ 9 W 3 40 3 la 45 = O + re it + l S) W Fufiddrx +0 CawS+VG\'V\*—Se 3(J,PJ$3: JPL*51‘ ‘ : O k(v0,(>lg\)= jp >l = 0 VC ‘ XVg + M V‘n @ ,9 :M =» Wk-M = -«P=° W W! C3) ,9 =2>\s => X’1/\5=0 <9 ,PLa-Sq'lf C9 JP ~I Fm @ w: an 1%» 3:57:31“! ji-O &u\c +0 @ 2)! :> "A@ s :- 2/\_Q PMsM® :5 s: L‘VXLS _ = 3:0 or >\‘1 i L 1.95:0 :3 >60 => «0=1‘! LIaM®UP=II fnm© 1:5; x=13£ :5 5:1’20 {Vt/MG) =>«o:1'_rl_;; CV'“®7P=: Sch) 1- SOME So.“ 3 5““ L} :5 m“ ‘ . 5:0 i=0! 5:}: s: -E (Q :l 1“ J0 : L “Q: _i P-'1 ‘ P3“ 7’: “’5 V p : ‘5: P ': :41; C: 1 C, ‘1 _; L- $351) a: 2,1164? +2) .. l: ..> Cos"? M‘KA‘VMte‘J ‘ 2% C: Whit; w/ SKUH=O [Hoar-l ...
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Wk6_Solutions - Worksheet 6: Prelim II Review 1) Estimate...

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