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Exam 3 &amp; Answer Key Fall 2009

# Exam 3 &amp; Answer Key Fall 2009 - Math 1552 E‘est 3...

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Unformatted text preview: Math 1552 E‘est 3 Name SHOW WORK FOR CREDIT? ' November 11, zone (Ledet) No Graphieg Calculators 1. Sketch the curve given by the parametric equations x : —2+ 1’, y = J1: . Indicate with an arrow the direction in which the curve is traced as tinereases. Eliminate the parameter to ﬁnd a Cartesian equation of the curve. (14 points) 2. Find parametric equations for the write given by 4x — ya = 5. (8 points) 3. A pm‘ametrie curve is given by CO?) = (t2 — 9, t2 —- 81?). Find the values of r and ﬁnd the (x, y) paﬁs where {12 points) A. the tangent iine is horizeetal. 2‘ vaiues (K, Y) 338.5(8) B. the tangent litre is vertical. rvaiiues (K, ﬁrm-11(8) 7. Suppose 13’ m (HS, 3}. Find avector parallel to 13, but not equal it) i. (4 paints) 4. Find the length ofthe path tmced by a particle on the euwe of :10?) 2 {sin 1?, cos {2) ever the interval? 1171' 55 t s 7. (10 points) 5. Sketch the curve given by the polar equation 7' = 1 + sin 9. Setup the integeai to ﬁnd the total area endosed by this shape. Yeu :19 not have to evaluate the integmi (12 paints) . . . (xﬁBY' 3:2 . 6. Graph the come sectien given by T + 3 m 1. (1.0 pomts) 8. Find the cmnponents of??? if? = (P3, 4, 7) and Q = (2, 9, 8). (6 points) 9. Suppose T533 m (2, —S, 4}. (12 points) A. Find the magnitude ofﬁﬁ E. Find the unit vector that points in the same direction as ﬁg} C. Find the unit vector that points in the opposite directicn of ﬁg” 10. Find a vector equation and parametric equétions for the line through (33 —1, 4) and parallel to the vector <~ 2, 1, 3) (12 points) BONUS: (2 paints each) 1. Who won the Worm Serias this year? 7 2. What is the 2009 win/i033 record for the New Orieans Saints? Math 1352'Tesii Nam; _, 7_ SHOW WORK FOR CREDIT! Navemher H, 2009 (Leda) N0 Graphing Calculating !, Sketch the curve given by the pamme‘rric equations ,1' : 724-1, .1” = if 1‘ . indicate with an arrow ihﬁ: direclion in which {he curve is iraczed as r increases. Eliminate {he-parameter 10 ﬁnd a Cartesian equation OFIhc cum/:3"; (1.4 poinis) if ‘5" [ LA" 3 ‘7; #1 {f if U] :A J: - ,_ m ._. k i in ~ 1 i3 \- ‘- 2 TL ' if”) (I; i i ___i__ _,_ >T . if?" , \ 2 /-v—.1"’- — \ I U H; J \I; Tia-OZ if j g} .3 A w \ i j] i 9:33) L ‘— i 5. L ’ I i “ L ___ i Li 1 i A )1 Tgf_,y,.,r—:_ { L31 \_ X ‘i '2, 2. Find parametric equations far {ha curve given by 41‘ — yz : S. (8 paints) 1. T. {'3 3—." LIF— F .T x. “—t C: 3. A parametric curve is given by C(f) = {t2 — 9, 22 ﬂ 8t}. Find the. values of I and ﬁnd E1130; )2) pairs wiisre (12 poi nts) ' 0U .- 3f ' g A. the tangent line is horizoniaf. I}; ‘” 9“,; i vaiues Li- . gilt A 3i“; .. 7 . .' . ‘— \,-~ ’ ‘ LL]. “ L) 5'. -: (71 i A" E] r; H 1] UH» (x, y) pair(s) (ﬂ?_:_'_mi_i__~) :24; 5 u it Mr"? 3-: m a i. 1‘ (3% x: ’i 31 “:H» B. the tangent iiiiais vertical. Names 0 ___ , 13 ,, « TTT“—. .i-iir'ulrvk l; - i " -.- 5L}. " “(9K 1 _ .— \"" riff. ‘5 LL (4” (31)}Pa1f(5) °i_ (3L 1 \ 1 ‘ 2% U y; 2‘ U "‘3 x3 :- ri w'gm £1. L: if _ 0i 3? i} 7. Suppose 1'? z: (—213). Find 22. veutor paralld 10 13, but not aqua} {0 1?, (4-? poinis) _ :1 ,5 _ K \1 K MU} 13> 4 Tind the Iengih of 111913a2htraced by a paﬁicle on the curve of r. (t): {sin 1“ 1265 t) overlhe interval i'hr g < L i "“6“ _ (:3 1301113) 7 3 -=- gm 6 Yr” {Li-s i" “‘13! 1; __M__rg___,.-'—A 1'11l =— Uﬁ. ’C ‘j r ‘2 .7 S 1 1’1 "1 1‘7, '2. . , '1, 1 _ V 1- _ A . 1 {If g \/ (6,310 if ( s1 1 ) Hr f": A 1f“ 7 5 G " x 1/1 ti: m 1 “I“ ‘1’“ 1+ ' 11111 ”'1‘ ’ *3“ 1 1, ,/ ,_ a 3 f7 .- € 1\ 1‘1 “/J/ I] Mr— ﬂ ‘—_, frz—ri ‘ " LEE— ? “I 1 H //’ """ : H,” r- if ‘ '13 6.. a) n], r “H ‘3 " ' ‘ ’ ’“ 3 5 Sketch the curve given by the polar equation 3 5 l + sin 0. Setup ii —:_;.- enclased by this shape You {it} not have. to evafuate the izztegra]. (12 point;) “L ”'\ fl \\ - , S {(E:W L19 d \-\ \ U _ él—ﬂx‘ Q \‘.- 1 _ 7 t (z— a); y* . 6 Graph the 691151: section given by + - = 1. (ii) 9011113) 16 9 g Q46"? 5 "L , ,_/ “i ,_ , _ (33 ‘37 CLA‘J_€.I/ ( 5) 0 > 3. Find the con‘qjaonenis ofiTQ‘ ifP = (-3, 4, '1) and O = ('2 0 8). (a points) I P: < ,3; ~ {—-""=‘) o— "l - 2> F-_.Wﬂ___ ‘ ._~___ ,HW_ ,W __-.._ W n_.__ __ 9 SupposeP 2(2, —5 4). (12 points) A. 1‘ ml the magnitude of {Ti}. ______ _W ‘ 7.:2'3 I "TE—ﬂ??? \3‘1}? 2 3 J L; H Y El r x 2- t .k I) _. ‘__ WW”... -—“—“*4' _" J , VT I) _ C" L \\ : JHL +231 U.- vL'r‘? / 3.; ”W .L \ r’” F? _. . . . . , W, vav \thg \i 9K B. had £116: umt vector that pomis m the same dlrec’non as PG. 1 _NJ / <1 I f H>7: 7; _ ":_ ____ " “ﬂu“ . T.” Lt ‘T - \ J3? ‘5 *5 V L’ r 1'2; '1? _, ‘lﬁ C. Find {he unit vector that points in the opposite direction ofﬁj ' * VLF-”Ea: } 613%) 1 H? 10. Find a vector equation and parameiric equations for the ﬁne thmugh {3, —1, 4)a11c£ paraﬁel to the vector (— 2, I, 3) I 13% *1) (UH-v5 H> " <6L'meﬁ>’i’ W -sﬁﬂ 7—‘Wwaiﬁf ﬁﬂkm ‘ (a. L} -::.> '3 <% 4‘ qPAkﬁ < xx, -' ‘_ L- ’HIW. 'LWW -—~- . WW _ _ (1 2 points) BONUS: (2 points each) 1. Who won the World Sen'es this year? Né’w 70" [-ﬁ- _ 2. “mat is the current 2009 winﬂoss record for theNew Orleans Saints? ...
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