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Test 3 Key

# Test 3 Key - Test 3{E3 Name Printed No calculators etc Show...

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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 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:... -u 2» am we 5‘» a rKA—ur M D M2 Hui-KIM? j’ﬁlm H307)" Ll <€ b) Find the limit if it exists. If it does not exist write “DNE” (no work necessary). 4_ 4 (5) ( linlo 0) :2 + :2 @ (Ely a 7 7. '2 Z Eﬁpﬁeg X ‘1 M9. )ml “3 '4‘ 4 ll __,_ (l’m' j I XL.” c =- Ilcwl’ : 21mm) H 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)t) ~ (,3: 0;) H22!) ’ ) f are m&‘ a. unli‘ Va/‘i'n C3 VFW an<blﬁ> :0 o r _,_\ <ﬂﬂ> :: < :1... —L‘ > I 7"“ U“ “Apt! ‘51?) «)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 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 .———‘7_ [out 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 +2.2-A3%_2_gj ﬂcju/ﬂca—cl- I; ﬁtXﬁﬂ-‘EV-e [S (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 (cad U <0)C>> ‘ ‘P(D’ O) :0 Pvtowcam #9} 10:21 X 4t° “\$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 y 3 a) The volume of the solid lying under S and over D. D , b) The surface area of the region on S lying over R = {(10, y) : 0 < :1: < 1, 0 < y < 2} 6. Find e‘mhy2 dA where D = {(113, 3/) :\$2 + y2 S 4} (7) 7L5 [AIM Coot-“4135,14. 211' :22 z 7. -—= m :J ﬂéL O 277 ._ __ ;§<«—:é'+:>w ’“ 7. //f(x,y)dA = ([myﬂmmx) dy D a) Sketch D (label key points) ...
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