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Unformatted text preview: Test 3 {E3 Name  Printed No calculators, etc. Show your work on #2—7. Circle your answers. Put all work on this
test paper. Maximum score = 73 1. a) Let f (50’) be deﬁned on a domain D in R3. Let f0 6 R3 and assume that D contains
points arbitrarily close to 330. Let L be a real number. Deﬁne precisely w) lmfm=L 7:“ «a e>o am we 5‘» a
Mar )7 M D M2 HuiKIM? 74in H307)" Ll <€ b) Find the limit if it exists. If it does not exist write “DNE” (no work necessary). 4_ 4
(5) ( iinio 0) :2 + :2 @
(Ely "—’ 7
7. '2 Z t1 2.
Jo x'l’vb' s. 2‘ ““9”“ :_ 21109?” 2. Let f(:1:,y) = $312 — 2m a) Find ﬁﬂx, y) (3) *5
\7 H m> ; b) Findﬂ’so that Dﬁf(2,1)=0 ~—3
—> .\ W9 v H2 o = <4 LI>
V.F[2)l) ~ (,3: 0;? H22!) ’ ) f we vii“ a. unli‘ ch‘l'vL C3 ”Vi/ﬂ (7f..<—Iﬁ> :0 o r _,_\ <ﬂﬂ> :: < :1... —L‘ > ﬂit: I 7““ U“ “Apt! a?) «)1: <1?! 55‘.)
Absent/Cr c) The surface given by the graph of f is sliced perpendicular to the x—y plane at
(2,1) in the direction towards the point (5,4). Find the equation in R3 of the #1:,“7 tangent line to the cross section thus obtained at (2, 1, W ,1. (CO rW/’
(7) ~——~3
A} v 3 <9)” * <ZH>= G) D
—3 “—37—
10.? u~ V = <3L;)Jﬁ> W“ 1757” 3. Find the equation of the tangent plane to the surface 3:2 +22 2 x+2y+32 at (3, 2, 1). LIJQ— ?(XﬁLQ); X‘X +2.2A3%_2_gj
ﬂcjmfkc4 I; ﬁtXﬁﬂ‘EVe [S le?)l)l) (7) 4. Find and classify as local max, local min or saddle point all critical points of   _ ._Z Z
f(m,y)=:zs1ny 1n D—{(w,y). 2 <y< 2} 2 <O/6> FF load f+ U <0)C>> ‘ ‘P(D’ O) :0
Prison/tam #9} 10:21 X ”5° “$31”; + 5. Let S be the surface given by the graph of z = 1 + 11:2 + 4312. Let D be the region in the :r—y plane bounded by y = a: + 1 and y = $2 — 1. Express as an iterated double )
integral but do not evaluate. . (2 ) 3 a) The volume of the solid lying under S and over D. D , (7) WA “mac/i 6. Find /D/e ”32—1/2 dA whereD= {(113, y): w 2+3123 4} mfkngziz [3:144 CboFan/xq‘j'ea, 271,6122 jfje rﬁr1’9& :2] iérz‘) 0 £& 7.] f(x,y)dA=/e:([lnyf(x,y>dx)dy
D a) Sketch D (label key points) ...
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 Fall '07
 Sadler

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