a5 - Jonathan Kim Assignment A5 MATH141, Winter 2008 You...

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Unformatted text preview: Jonathan Kim Assignment A5 MATH141, Winter 2008 You may attempt each problem a maximum of 5 times. Please remember that, while WeBWorK can usually check only the correctness of your answers, your responsibility in this course is to be able to justify your answers to problems of all these types, and others. The assignment is due Monday, March 24, 2008, at 11:30 PM. 1.(1 pt) For each set of Cartesian coordinates x y , match the equivalent set of Polar coordinates r . 1. 2. 3. 4. A. B. C. D. ( -2.3 , 7.6 ) ( 1.3 , 1.7 ) ( -2 , 8.6 ) ( 2 , 9.2 ) 2.(1 pt) Consider the parametric curve given by the equations Correct Answers: 3.(1 pt) Find the length of the parametrized curve given by 56.5685424949238 13 4.(1 pt) Determine the area of the region enclosed by the astroid x 4 cos3 18.8495559215388 1 Correct Answers: y 4 sin3 for t between 0 and 1: Hint: ds is a quadratic polynomial with integer coefficients. dt Correct Answers: yt 1t 3 3t 2 9t xt 0t 3 6t 2 12t How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=8 ? yt t2 4t 28 xt t2 4t 26 A C B D Correct Answers: 7 9404 8 8295 2 1401 9 4149 1 8647 1 7993 0 9179 1 3567 y 16 sin3 is called an astroid (sketch it to determine why!) Find the total arc length of this astroid: Correct Answers: 96 6.(1 pt) Decide if the points given in polar coordinates are the same. If so, enter T. If not, enter F. 6 6 3 3 2 43 2 43 4 4 0 6 0 5 4 1 125 1 4 4 6 62 6 3 3 6 10 6 10 Correct Answers: F F T T T F 7.(1 pt) For each set of Polar coordinates in 1. to 6., match the approximately equivalent set of Cartesian coordinates in A. to F. 1. 6 6287 0 1974 2. 5 3000 2 5850 3. 11 1508 2 0866 4. 4 3139 0 8018 5. 10 2694 0 3895 6. 6 2936 0 7742 A. 55 97 B. 4 5 4 4 C. 9 5 3 9 D. 45 28 E. 6 5 1 3 F. 3 3 1 Correct Answers: E D A F C x 5.(1 pt) The curve defined by: 16 cos3 Correct Answers: 10.(1 pt) The parametric curve 12.8281700021583 xt yt 2 cos t and 16.(1 pt) Determine the area of the region enclosed by the limacon 11.(1 pt) Determine the length of the spiral for between 3 and 7. Correct Answers: Correct Answers: 7.38905609893065 18.(1 pt) Determine the total arc length of the cardioid 40.8363160043798 Correct Answers: 0.6 2 Correct Answers: 56 an 12.(1 pt) Find the limit of the sequence 3n2 1n 7 as n : 5n2 3n 4 r 2 an by 17.(1 pt) Find the limit of the sequence whose terms are given e2n 6n 1 n 0 0 2 -2 Correct Answers: 119.380520836412 r 7 intersects itself at a point P x0 y0 where x0 and y0 . The slopes of the 2 tangents at this point are . Correct Answers: 2 sin 2t Correct Answers: 26.7035375555132 r 6 2 sin 7 sin r 7 cos 3 15.(1 pt) Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges to negative infinity, state your answer as "MINF". If it diverges without being infinity or negative infinity, state your answer as "DIV". 20 lim 17 arctan n2 n 3n 9.(1 pt) Determine the area of the region enclosed by one loop of the three-leaved rose Correct Answers: 2.1589759627383 What is the length of the curve between y 7 sin cos V L C R x 7 cos Correct Answers: 14.(1 pt) Consider the parametric curve sin 2 15 sin 1. 2. 3. 4. r r r r 1 15 cos 27 2 sin 15 cos Correct Answers: INF 8.(1 pt) Match each polar equation below to the best description. Possible answers are C,L,P,R,S,V,and Z. DESCRIPTIONS: C: Circle centered at the origin, L: Line neither vertical nor horizontal, P: Parabola, R: Circle not centered at the origin, S: Spiral, V: Vertical Line, Z: Horizontal Line POLAR EQUATIONS: B 13.(1 pt) Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity, state your answer as "INF" (without the quotation marks). If it diverges to negative infinity, state your answer as "MINF". If it diverges without being infinity or negative infinity, state your answer as "DIV". 8n7 sin2 7n lim n n6 9 0 and 1 4 ? Prepared by the WeBWorK group, Dept. of Mathematics, University of Rochester, c UR 3 1. r 3 3 sin 19.(1 pt) Match each polar equation below to the best description. Each answer should be C,F,I,O,or T. DESCRIPTIONS: C. Cardioid, F. Rose with four petals, I. Inwardly spiraling spiral, O. Outwardly spiraling spiral, T. Rose with three petals POLAR EQUATIONS: 2. r 17 sin2 3. r 3 cos 3 4. r 3 r 0 Correct Answers: C F T O ...
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This note was uploaded on 08/23/2008 for the course BIOL 111 taught by Professor Brianmcgill during the Fall '07 term at McGill.

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