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exam2_soln_F11 - Your Name Printed Clearly Wfl—i Justify...

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Unformatted text preview: Your Name Printed Clearly! Wfl—i Justify all answers! Show all work for partial credit! EXAM 1 o BOYLAND o CALCULUS 3 0 FALL 2011 1. (a) Find the directional derivative of f (any) 2 1331/2 in the direction 9 = 77/3 at the point (1, —2 . ()b) What is the maximal rate of change of f at the point (1, —2) and in what direction does it occur? 2; 3‘ g“ /-23: /.2 ”V7 Vglhq):<37‘7/ :r2><0>jvrfi\ (I < / Q r ['2 <j2/ '— elimii/O” “5 Wt” Uch ELL—2 N #m/ /’7§(,,2)/ PAT/3% 2. Find the volume of the solid that is bounded below by the paraboloid z— — 1:2 + 3/2 and above by the half— —cone 2 —— 2W. 2: 2 V V Im 90 \Cu/ TWO gag/S q Q 221/)”; . V: 2 ‘ iQVSeoT WW“ V1 - f or V 0/ , 43% W71 1% C)£ (~94 2N " :)\7{‘( Z ,_2)/" /‘/ +lo/‘7‘t/ A“) 37:00; Page 1 of 3 Total points this page out of 20 - 1T . - h 6 -V S621 9113“,; /Q:: 271/6 I ?Z 3. For the surface 251:2 — y2 + 322 = 10 and the specified point (2, 1, —1): (a) Find the equation of the tangent plane to the given surface at the specified point. (b) Find the equation of the normal line to the given surface at the specified point. 4. Find the volume of the largest rectangular box that can be placed in the first octant with three faces in the coordinate planes and one vertex on the plane 216 + 33/ + z = 6. V: >43 Q buff 23g" Qf‘gj . . ' Z - 2 \ :7 Vl‘fittfl: 4 5‘32“ tag-37 / 4 X 27‘ - 57‘j/ a cm pars we «Mues- w— 4 : mm 0 : \j [C‘ 7x “SJD é: affe‘jsb _. i ' ‘_ eeu- has YLG‘O Page20f3 0 y X [ é (2x Totallgoints this page out of 20 X :l _ CV47 Pot-4Tb 0W? [0/5” {0/ 1)] (Z: 0// ( [kl/3) (3-77.: V20 Sc Cal/rut be Mix (De-CM; 'nmz QWQ, _ . totem x:i,c7:Z/;/i’ 5. Evaluate the integral by reversing the order of integration. fife dxdy : 7- .) X 0 ‘39 O. :1 ’2. 2 ixgj SO x 6 9* x3'2 3 H (Q H \ 6. Let f (as, y) = 63:3; —- 2x3 — 2y3 — 4. Find all local maximum and minimum points and saddle points of f You must justify your answers with the second derivative test. WNW?) < 63 ~66 W 557.17 C19. 1T FOP/TB “86$ I)(”) )l) :Iaq-at 7C> V" 60 CriT pain. aka? ("/i'):"‘“0 [0/08 (ml Page 3 of 3 // b< Total points this page out of 20 60 L00 ‘ ...
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