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m251ex2key - MATH 251 Section 504 Test II A~K~ 1 2 3 4 5...

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Unformatted text preview: MATH 251 Section 504 Test II March 12, 2004 A~K~- 1. 2. 3. 4. 5. Total Name There are a total of 5 problems. 1. (a) Let Show that U = U(Xl,X2,... ,Xn), V = V(Xl,X2,... ,Xn). \7 ( ~ ) = U(\7V)- 2v(\7u) U2 U3. (10%) (10%) (0.) 'V(-& ) = (!x(~)~ ." . (J!:,J ...-LG V») = ( ",t.Il-U"!x.(v.~ u'l.~ "liktf~ u~ ""'/x,.<IAI.») IA ~ I '" )11 J. "J ) a"... f)..&') u+ J «+ J. ..; ~. / t..~tr- au 'L.JJl. 9'" &.~ ~ ~- ( t.\ ~- 2.V~ ~ &.(&"-2" 2.Vt.t ~ ... IA i)?C..-2.~ 'i'i(;- 144- , 1,.(4 > 1 1,.(+ ~_U,.(V~)~- US X2 (y-1)2 z2 (b) Derive the equation of the tangent plane to the cone 2"- b2 + 2" = at the a c. point (xQ,yO,zo)O'k ~ ~. ::::..!:L(~ 91t...' .!tL)- ~ ( 9~ ~ .., ~~ '\- u. \. ~I) ~'X...,.} ) !'''"j U~ 8",1 '''a.) ,I 7)7'",,- ~ ( '" -0"- 1.t. (h) L.&t (;r(~/'11lr)= ~a.-~ +7 :"d. L .::t (~/1,/~), ~ '1.1< ~-I 2."'"- ' V~t"''1'~)1 ::.( ~L)-~)-,,"- ( (~, 1" r.)' .J-1-' U'o.'t.;t..) ~ €.t~ ef 1!.c. t4~ r-4+'JL ~f~ V&("OI'1o/~)' (x-,co 1'1-~o 1r"~)~" J tt..) .,.<.~-I) 2. ~ 3-~: l'1C-><e»- - i ~ <.Lf-'1 o)t-: C 1. (roo~)=- 0, %x~ ~- ~ll.f .., ) f - 2.}'v 1.= !1x,- ~o- '2..('16-Y { '1-I' of. 1.~"t.. = 0."1 h2.h2....
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m251ex2key - MATH 251 Section 504 Test II A~K~ 1 2 3 4 5...

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