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2010 final fall

# 2010 final fall - AEMA 102 Calculus II FINAL EXAMINATION...

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Unformatted text preview: AEMA 102, Calculus II FINAL EXAMINATION Date: April 27, 2010 Examiners: Time: 14:00 - 17:00 Profs. J.F. Ha es and RJ. Cue Use of calculators is prohibited. -MW 1. Determine if each of the following sequences {an} converges or diverges. Show clearly how you arrive at your answer. 9 marks (a) { \/n2+2n ~n } (b) <c> {"23"} 2. Determine if each of the following series converges or diverges. Show clearly how you arrive - p at your answer. ' 15 marks 3 (a) )3 5’33 n22 ’1 (b) 2 3 "=3 n2-4 °° (-1)"*’<n+1) (0) mill ln(n+l) 0° 24:1 (d) "20 (2n+1)l (e) E ("0” n21 ("W2 * 3. Determine if each of the following series converges absolutely, conditionally, or diverges. Show clearly how you arrive at your answer. 9 marks °° (—1)" (a) X n = l 1171" (b) 2 100003 (n 11:) n 3 1 2n + 3 00 n! (c) 2 n n = l ("1 00) 4. Evaluate the following improper integrals. ' 1“ 12 marks (a) I: cosxdx 5. Evaluate the following integrals. 15 marks (a) [an x)3 dx (b) I sinzx coszx dx 1dx “4 (a) [F 6. Find the area of the region in the ﬁrst quadrant that lies inside both the circle r 2 l and the circle r 3 2 cos 9. 8 marks 7. Find the arc length ofthe graph of 1* =1 ~0058, 0 g 6 3% . 8 marks 8. Find all the points of horizontal and vertical tangency to the graph of xzcast, yzsin(2t), OstsZn. 7marks 9. The x— and y- coordinates of an object moving on a path are given by " x =cost +tsint, y :sint - tcost, 0 s is 7: (a) What is the initial speed and what is the ﬁnal speed of the object? 3 marks b) What is the distance travelled b the ob'ect? 6 marks ( y J r- 10. A portion of a sphere of radius 2 is removed by cutting out a circular cone with its vertex at , ‘ the centre of the sphere. Find the surface area removed from the sphere if the vertex of the cone forms an angle of 8126 —— . a _ 8 marks 3 ...
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