222-robbin-07spfin

# 222-robbin-07spfin - Name Math 222 Final Exam Thursday...

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Unformatted text preview: Name ____________ Math 222, Final Exam, Thursday May 17, 2007 Circle your section: 323 324 326 327 328 329 330 331 1.13 INGRAHAM B329 VAN VLECK B135 VAN VLECK 119 VAN VLECK B337 VAN VLECK B305 VAN VLECK 8329 VAN VLECK B333 VAN VLECK TR 08:50—09:40 TR 09:55—10:45 TR 11:00-11:50 TR 11:00—11:50 TR 12:05—12:55 TR 13:20—14:10 TR 14:25—15:15 TR-15230—16220 Georgiou, Nicos Georgiou, Nicos Ache, Antonio Beros, Achilles Ache, Antonio Beros, Constantinos Beros, Constantinos Beros, Achilles w l l 30 Points ll 30 Points i ﬂ J. 111 30 Points IV 30 Points ' ~ 7— + 7+ *r V 30 Points VI 30 Points VII 30 Points Vlll 30 Points l— 1 l— ———+ l————— lIX 30 Points 30 Points ‘7 T :F 5—: a“ Total 300 Points L i SHOW YOUR REASONING. 4 if03\$<1, 1 2 I. 30 oints. Find / cc dx wh = :c ( p > 0 ﬂ ) ere f(\$) {:55 if 1 g x g 2. 7 1 d3: 1 \/4-—\$2. II. (30 points.) Find/ CESCILI? 5232—1. III. (30 points.) Find/ IV. (30 points.) Find y if _'y — y = 27 y(0) = 1 and y’(0) = 3. V. (30 points.) Rabbits in Madison have a birth rate of 5% per year and a death rate (from old age) of 2% per year. Each year 700 rabbits move in from Sun Prairie. (i) Write a differential equation which describes Madison’s rabbit population P at time t. (ii) If there were 12,000 rabbits in Madison in 2001, how many are there in 2007? d2 ‘ IV. (30 points.) Find y if d—tg: — y = 2, y(0) = 1 and y’(0) = 3. VII. (30 points.) Given the vectors 2 ii = 1 and 3 ﬁnd it, y, for which ‘ a = :7: + :7) with :7: parallel to 3 and ﬂ perpendicular to (3. 0‘1 H l—-‘ VIII. (30 points.) Consider the following parametrized curxre: 1 (fl/3 _ _9_t5/3 55(t)=( 7520 > o'gtgi. Find all points with horizontal or vertical tangents. Then ﬁnd the length of the piece of this curve corresponding to the indicated parameter interval. IX. (30 points.) Find the curvature FL of the ellipse {ti = 4COSt; + 3sint3 at the points 14(470) and B(0, 4). X. (30 points.) A curve has polar equation 6 T: 3+0056‘ Express its position vector :73 = mil—5623 as a vector valued function of 6 and sketch the curve in the.(m1,3:2) plane. Indicate on your graph Where the curve is farthest from the origin and Where it is closest. ...
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