# QUIZ 08 - Quiz # 8 Sections 14.8-15.1 (15 points) Math 200...

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Unformatted text preview: Quiz # 8 Sections 14.8-15.1 (15 points) Math 200 Name: K43. 1 03/22/10 Show all necessary work for credit. Group: 412125.]. UseLagrange multipliers to ﬁnd the maximum and minimum values of the function f (x, y)=%+% subject to the constraint x1—2+%=1? Conshairct I ‘2} {53] = “is + ﬁn. =l — -1 .1 _ _i_ _ 2-. v+'<x‘)”7z) ) *( x1) 73> Lo arrange Cant-Vim. : 7‘ U .. .L_ .. _. 12 _\_ 3 x“ a? =3>x= 2x339”) r_i ax- _ __ a a _ _ l a 7‘ ' 3-7 “ ' 7 71 7-; —> X " a. y ) o Sukg-l-i'l’u‘l‘e {n+0 -H~e git HF : 1 (oust-raw await“: . . 'iﬁifﬁl =3 x"=1 => xvi ti. CY‘I'H‘ULl {loud-.5 ‘. (0—52) 53.)) (4531-15,) )I:i 03. - _.L . ﬁ ﬁ 2 U3- ‘TlNQ MMImUw‘ value .‘5 : J1 _ _\__ _. _ . . _ H" Ltiii—JET, i-lr‘l a ' ‘03. Tine mmCMh. value 15 "His-fa) - ‘ﬁ- 3 pts. 2. Use Lagrange multipliers to ﬁnd the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid 9::2 +4 y2 +922 = 324 . C °n5+rmk+: Jay 71%) =_ 9x :- q; + \$21.: 5:” VV= 1‘13 U =(18x9 18's) ? 2 ﬂ :9}; 3 2 7) 7% “3x A p.) A x Detail? +lxe ward-ices ell-Hm ‘00)! 3x2: 8’ l => : 8x = ‘3); A u A ‘07 (ix/1'), 1%)) when 30/720,320 I L 1 "a )1 1?: "The volume 1'5 'ervx “1;: “+7 +°t2 :3” meal = (1200,0119: 3x72 _. 3. - 1.1% = :3 wyzﬂh‘L :0 y -1: 2x .4 VU ' <97E) 3X11) 3X7) F _ I\‘ a.l {6:41 {i 4- Hez‘ﬁr—n 2-131 nan-1x a" f l” 35/“? 1‘10? vb at; MMMM value: Vf‘lﬁ)?)\J—j/Qy’§j; 1. 1. d?- uolu e. qxx+ﬁli%x)+°((ix) :‘32'1 “:1 Cle+°th+?x‘=3?-~t 1')X311ﬁ2y=—a(2f§)=i3ﬁ,2=il@ 2 pts. 3. Use the Midpoint Rule (using 4 rectangles) to estimate the volume of the solid that lies above the square R = [0,4] x[0, 4] and below the elliptic paraboloid f (x, y) = 68 ~ 2::2 — 2 y2 ox: t§=2 0y: i327“) new Tun?» ,y.-=1,3 1. 1- 2. v: {Nihqm‘t 1—“ 3m = Eitmﬁzlaa k=15=| : [Hunt—Hun1—5}(3,i)+¥[3,2)] 13A : Egg-l + as +qa+321-L+ : ﬁnd—i : 758 2 2 pts. 4. Evaluate the double integral of the function f (x, y) = %+ gm)” am .13; 3" x2 1 .5. ‘1 y 3 Ema; +Ijif 1 1 = on. 1 9 2 .j 7 .f)‘ “Tf7d7‘l % 1 I 3 I 3 1 1 EM 3"l. “:7 li'l‘ﬁll = 3—2,. 19... ‘ .1 3 W: a) wit—mam vim“. 2_pis_.5. Evaluate the integral I I y dydx 001+ch2 l I 3 1 j ’1”— d d 3; ‘ 3 __ l 1 ‘ cafe—11;; H “ﬁt—WM” fy’lL—L“; dv 0 ﬁne l y I 2 1. ?. 'fQYOlWLJﬂdy ~ EM?) 7 O 0 .. 2 % 2 ‘i LH/i-S "EDP"? :Efl'Jé “r 3 11 m 6. Evaluate the integral l+y4 ln(l+y2)sin(xy)dydx . 57‘ —10 I 1 ‘1 2‘ 'h 2 _. 0 0”? “(H7 5 3‘ {WWW bf‘fmjmﬂ‘tvan-‘(xﬂdxdy :j HWJOJH ~ic 5 bl 6 < 7>X~7 b ()7;ij \ :Jd H't/Hjm (1+?) ";<_.(057+ (oS(-y)) l : jealy [Same C05 (“7): (057 over the rectangle R = [1,2] x [1,3]. ...
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## This note was uploaded on 02/24/2011 for the course MATH 200 taught by Professor Jamesdcampbell during the Spring '10 term at Santa Barbara City.

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QUIZ 08 - Quiz # 8 Sections 14.8-15.1 (15 points) Math 200...

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