Math2015_09_T2_Solns

# Math2015_09_T2_Solns - ZS Wmt‘lég Math 2015 Applied...

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Unformatted text preview: ZS Wmt‘lég , Math 2015 Applied Multivariate and Vector Calculus: Test2 Friday October 9, 2009 10:30am to 11:20am Name: gOLUT 1,0935 Student Number: Instructions: Complete all 5 of the following problems in the space provided. Notes and calculators are not permitted. All cell phones and pagers are to be turned off. 1. The radius of a right circular cone is increasing at a rate of 1/2 in/s while its height. is decreasing at a rate of 2 in /s. At what rate is the volume of the cone changing when the radius is 12 in and the height is 10 in? (Hint: the volume of a cone is V = 7rr2h/3). a Li V:'LTU\‘7'\rt grads: 3 CW Tl“ iLr‘lﬁ tr 2 a = - = __ thdc c Ala ’— db 5 at sl 3; J“ a} CD (TWUA Al): +1 \3 (lk‘="2‘_‘:’1 ® at: Z 3 dt 3 u l% ,_. c F 6° :a U‘ \_/ (l " 56w h‘nS/3 2. Find the limit if it exists, or show that the limit does not exist for cases 5 writs a (a) lim xycosy 1'4 _y4 d b 1 (1: y),)—+(00 )3x2+y2 an ( ) 1m (2: ryHOO) 1'2 + 1/2 (0) Le]: 1901.53: X30255 So ?LN,)L)-—’> \ 0A (1,3L)~3W,o) . mg ’m hm owe mt 14:34~ MG) (53 Lo’c yang}: Eddy 5L1¥KL r (28’ 17/30‘74/1) LEE/>46) Ms &\W\ #01”): 0 (plus) --3 00,0) 6 ' ® 2 1w?) “Q3 3. Determine the tangent plane and normal line to the surface S W 1L5 \$3 +3rzyz + 2113 — Z3 2 ‘15 at the point (1, ~1, 2). Lalo Fungﬂ): 13 + he? + 2:33 ~— ‘13 Tu mode/"r pm act FW'JF Fp 010mm cs awe/n Ebb VFW». ‘6“:5'0‘) ., LJ-‘Fo 1 = 0 (ANN F: 0M5.%). mepvh M ﬁendumrz VF = (%xz+3\3;)1 + (311+ bBWSJr Birgi')? “(D Hm vat—m) ~= (Maxi + (WAS HJs-mi = «men’s—1512 -—--—® 3mm, (\$411,): (l"2‘3*‘3%—Z> (ML Wﬁw‘l‘ p‘MLfS (—3,|2.-Is)o(1~\,5+1,%—23 : o “(D ~3(&I)+n(5+0~1§£%~23:° Kg) {’WJMU I M Mrwwdl lime vs @9933 written as 3.1:): W : afi} 3 4. The function f(:c,y) at the point (1, 2) has a directional derivative equal to 2 in the direction towards (2, 2) and equal to -2 in the direction towards (1, 1). What is the direc- . _ ‘. . . . . ‘2 . q tional delivative in the direction towards (2, 3). g 5M0“ k5 ‘ A LCt E: [2432 1 (2-1): ; 1 \$0 WM vied-b, i's - " A _. EZ‘ : —A “V“ A W, N!— chw‘ DQ‘HML): = ’L'Vﬁlm‘) ”’0 U r—4 3" 4— N r...) H l—P 5. Consider the function z : f(:c,y) Where :L’ = 5 + t and y = 5 — t. Show that Emarks , <6z>2 _ 82>2 _ azaz a (87; — 8—55 33 ﬁt Chum \Zvlu bl: [email protected]_¢+§%:?§ ~© (OS 2)}, ‘Dﬁ ‘93 )\$ 32-: 212.22»:- 222:: __ '3‘: Blobtfbgb‘l: (D Smu, x: \$44; M34 3:9-‘t git: i 33} : 1 9t 9% (D 2‘5: ‘" 2H -' \ “0t 9% Hand, {a}; z 2} + '33 25 31 53 L9 (Di: 94.1; "' (a? D» D» DI; Thus Qk‘Qg; ~(D_&+‘Q} [8}:2} 79\$ 3*: 7”“ 93 ...
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