1999 Calc 3- Exam 1 Solutions

# 1999 Calc 3- Exam 1 Solutions - Fa H I a c7 C7 . . MA'261...

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Unformatted text preview: Fa H I a c7 C7 . . MA'261 EXAMl Name (Lit/ii O n ( ) 1. Find the equ_ati0_n of the p1_ane containing 0, 1, 2 and whose normal is perpendicular tobotha=i+j,b=j~k. U «7 if» ‘7”- “ A. \$+y+Z=3 N: ax L9 :’L+J+k‘{l”/,) @—x+y+z=3 C. m—y—z=3 Eoumtl'on 013 ﬁle flax/he VJ!" "9 D. \$+y+z=—3 {in}. VLOV‘Mlz A/ C0W{£U"U'“J (‘2’): E. None ofthe above (-/)-x+ 1134) + /' (3’2) ’5’ .__>( +; 4 Z :3 2. The distance between the plane 253 + y + 22 = 4 and the point (1, 7, 2) is Laeé P:(l)7)2)l A.1 , B.2 @3 D.4 ﬁslz, )l. l) [.5 A MVMJ vet V‘ E. None ofthe above to w: ﬂew; .9, [A7 POP} 9 MA 261 TEST 1 Name 3. A unit tangent vector to the graph of y = 2x3 at (1, 2) is given by PRprfdfe'irt'L e7uR/7LI‘OM3 5 gig; .: 3 E —' y 275 ‘ B. 3% The FOCMf» [1’ Z) (or/“(S/ﬂomJS ;_3 A, C Takyew’l Vet/‘9‘” 7E0!) 79:10“) 22/:33 .7 D. Af .621) Tz/‘l/ 37 7:? / «‘7 E z 3 UN skim viewer T/m/ “5 gauge/Kg 0377 4. A particle is moving with acceleration 43 + 61512. If the position at time t : 1 is F(1) = z'+ 33' + k and the velocity at time t = 0 is 27(0) 2 z' + 3', then the position at time t = 2 is ‘7 ’ 7’ ‘7 A- 4i+103+1oze ' L/ J + 6 f B. “434F101; +5 r: C. E+§j+4k a) ‘7 2i+103+8k "It 37 1+ 3tz [4 t ' C r w A 7’ F." ’9 '7’ 5-Cch 0’10) rH—J C Il ﬂ} 7 2 ‘7 '” q 7 '7 +2 VZH”\§U’[1‘)9H+CI I: it +/z{1¢{)j+.£3k + C] Sm“ FU)~’T+\$?+I¢, Cftﬂi Hum F(z):2‘z’rm/' +314 2 MA 261 TEST 1 Name x2 5. Which of the following surfaces represents the graph of z = — + 3/2 in the lst octant. E HL‘PTKC qu Loo [act MA 261 TEST 1 Name 3:102 + 3/10 , . 6. If f(m,y) = \$2 +y2 , (3:,y) yé (0,0), let E be the hunt of f(x,y) as (110,31) —> (0,0) along the y—axis, and let m be the limit of f(:z:,y) as (33,31) —+ (0,0) along the line y = m. Then O A.£:3, :2 Z: KM“ WW7): 6”“ ’2‘0 @2:0 2: 3470 7-?0 ’ 3 C €20, m=§ 2. . r a Li); ’ D e=3, m=3 m: ﬁbsx) X63; ZXZ-Z‘ E 32%, m=% _7 7. Find a value of a for which the function z : 4COS(.’IZ + ay) satisﬁes (922 8% 87229555. A. a=2 (58,—: : —L/Sﬁ4 B. a=0 C. (12% 2:2 _: »L1coS (20%;) 13- 0:1 ox‘ @a=3 (a; : ,L/Q‘S‘h/X’f‘ayj 9 (all? : ’ (1&2 cos (Xifag) of ’2_ azi 3 a :9, MA 261 TEST 1 Name 8. Find the maximal directional derivative of at (1,1,—1). 9. Find symmetric equations of the line containing (1,2,3) and perpendicular to the plane 2:3 + 321 — z = 8. NOVMdZ VWW YLI? l/Qaue AZ‘KZ. 3’9 Symw-ta wit/‘12. e7auc 711.014 3’ a! (aw/14'“ [(7 (h 2‘ 3) mm loam/2e K 74; [2, g, ’1) awe >_<;;l_ : :11: £2 2, »I MA 261 TEST 1 Name 10. Find the length of the curve 2 — _ 3 _ ﬁt): %i+7j+%k,0§t§2. M24: + {112’ n F’m/I: hsz a 2 5* ‘ L .» yaw/(aim: 50 -£ Jam/i :E’ g! minimal . 2 31/5” *1) ) 11- (a) Complete the following deﬁnition of fy at (0,0 : fy(0, 0) = lim h—>O L” M 0 0 (b) If f(a:,y) = { 3m2+4yz’ (x’y) #( ’ ), compute fy(0,0) by evaluating the 0, (at, y) = (0, 0) above limit. MA 261 TEST 1 Name 12. A right circular cylinder has a radius and altitude that vary with time. At a certain instant the altitude is increasing at 0.5 ft / sec and the radius is decreasing at 0.2 ft / sec. How fast is the volume changing if at this time the radius is 20 feet and the altitude is 60 feet. V: f/‘VW A / armrme 77M : d, 277.2(9‘(>o.z)'60 +7T'30 '05; +200):“23707f ﬁll/36C ,5. 3 Lr‘ZXO W 12+{e ...
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## This test prep was uploaded on 04/07/2008 for the course MA 261 taught by Professor Stefanov during the Spring '08 term at Purdue University-West Lafayette.

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1999 Calc 3- Exam 1 Solutions - Fa H I a c7 C7 . . MA'261...

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