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# exam1_sol - MA 174 EXAM I SHOW ALL YOUR WORK NO CALCULATORS...

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Unformatted text preview: MA 174 EXAM I 02/18/2011 SHOW ALL YOUR WORK. NO CALCULATORS, BOOKS, OR PAPERS ARE ALLOWED. N ame: PUID: _______..___ Section: Points awarded (T1 1. (7 points) 5. (24 points) 2. (7 points) 8 6. (12 points) 3. (7 points) ’9) 7. (12 points) 4. (16 points) 8. (15 points) Total Points: 1. (7 points) If L 2 lim W, (m,y,z>—>(0,0.0) :6 + y + Z then A. L = 1 B. L = ——1 C. L = ~—2 D. L=0 w )(JWD L>l E.‘ the limit does not exist ﬂ-W5 L:-[ 2mm L‘2-7/ 2. (7 points) The surface deﬁned by 22 = 43:2 + 9y2 is a A. hyperbolic paraboloid (B .I elliptical cone elliptical paraboloid D. ellipsoid E. hyperboloid 3. (7 points) Which of the following statements are true for nonzero vectors u and v? (i) if u - v = 0, then u and v are orthogonal (ii) if u x v = 0, then u and v are orthogonal (iii) 11 . Projuv = 0 (iv) 11 X Projuv = 0 A. (i) and (iii) only E] (i) and (iv) only C (ii) and (iii) only D. (ii) and (iv) only E. all are true 3 3 3 3 3 3 3 3 3 3 E 3 3 3 4. (a)(10 points) Find the plane determined by the lines a: = t, y = ——t + 2, z = t + 1 and x:2s+2, y=s+3, z=55+6. DR PU’ 2.33 ,EIQ/s W'bﬂ 23mm ) 77W“ 't ‘0 311\$” W (7% NW 4 J J ‘5 4 3 J K A {\‘x u PAW/"\$43 % ‘50» PIN v3 V13“); - ’ , :-I)L*5J‘+3k i .. :2, r S TLMW f/w \/:) ’bx—%y+s2<»é(°>-3(z>+;u>: -3 ‘ IM3 pnlc M Pen/tit an "—5 (2X+Y~E:]‘ WW ”3 Mﬁwzbum‘ #umwm.pik (b)(6 points) Find the distanee from pointS 3,3,2 to the plane in a. ( I; I 7/) ( ) U P 2 Ct)» . 3.3 3333 ?s w. <3-0,3’1)w9> :0, "/3 J \5 ‘ (3’))’>&< 2),) “’> 3,33 3 1 I ’ ~ ,4 J .____.._.———-—-—/ 1 w : o4 : \$3 H I733) ‘J 21+)Z+(«I)"L 5. Let r(t)=(2+t) i+(t2+3)j+(§t3—-5) k. (a)(8 points) Find the parametric equation for the tangent line to the curve r(t) at t = 3. SJ: ﬁg): £3+I2F+I3k ’pmzt (‘33/2’12/3) NS .4 p-\ W153” g +2tj+zt1k \s 1’ ‘3 “J Vu') : L +6)“ +!&l< WWIMJN‘S ﬁw ~514me (b) (8 points) Find the arc length of r(t) from t = 0 to t = 3. .4 ..> ‘4 \$31? 7 {ft-Jo): CHM/t J” ~+ ztzk [\7] 2] 1+ (at)? (17591 1 J /+ ctﬂwt“ —= if?) ‘\ g:f_\$ NW? : [fathom :. fiat}; :— [8+3 :3; (c)(8 points) Calculate the tangential and normal components of the acceleration. 34 E, g E r E E E E E E E E E E 9 E E 6. (12 points) A particle starts at the origin with initial velocity i— j+§ k. Its acceleration is 2 i+ 4j + 2t k. Find its position at t = 1. 8% “‘ git): 2/? Jrin +ztl: \kvl I ‘3 Q NA N) l, T) int): [(Llﬂ‘i'SLJS‘I’Lf/C )dit : lit Til/ff4f [(+C/ 1% Y3éﬁ): JEZE+))?+(LLtVI)§ +(itl‘t ,:;> K] at \ o i z i; I 9 2 o J :(t24t)t\ +(2t‘£)<) ”+(‘gt+~j-JC)K +62, 4 a A w 0 21> CL: D Q 2 1% Yl€>’( (1;th)? +(ztz— DJ l(§let+ Jc)/< 7. (12 points) Find 3—: and 3—; at (1,1,1) if 2(90, y) is deﬁned by the equation zB—ny—yz—y3+3=0. g 3 33 3 3 3 3 3 3 3 3 8. (15 points) Let C be the intersection of 332 + y2 2 4 and z = 5, ﬁnd the curvature and torsion of C at (2,0, 5). ¢ ‘5‘ i *3 ”A S93 0 m): 20% C 3+ amt)“ +f/C Wham“ WM? :5 Mai . «3 5%): "lb/vi}: 5!! 2mm“ Q :J A ‘ i J L .\ 03y; : /-~M;t wt 0 : Qik :\ ){jxij/ : (7L «wt VZ/Vf 0 I 3 ~2§J£ gwt o I E/ ~mt ~Lyt 0 T/c 0" :: 23mg: "\$6V3f 0 O [7312/1 :— xx) 15 \J ~Z£f C “I‘M/03%) \i Q LL ;; I‘LVt (“/‘Onij 0” [diva/t} .. 4 : Ki M7); _ 2’ J OWE/0'5 “3 :5 1 .- ~ wa6 A) ‘ idf/rw M J A «3 A \ \ V \j x)” l) ‘3 ‘ I 0‘ \ 7‘) ﬂ oils _\ IE“!)U\) ., “31+, Ont 7D :: )’\ 50(t:o «B “(Mic 'L‘f 0 01/1: ,3 ’Dtr-m” :_ ...
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exam1_sol - MA 174 EXAM I SHOW ALL YOUR WORK NO CALCULATORS...

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