m251ex2key - MATH 251 Section 504 Test II March 12, 2004...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

This note was uploaded on 07/21/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

Page1 / 5

m251ex2key - MATH 251 Section 504 Test II March 12, 2004...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online