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Unformatted text preview: AEMA 102, Calculus II FINAL EXAMINATION Date: April 21, 2008 Examiners: Profs. J.F. Ha es and R.I. Cue Time: 9:00 - 12:00 Use of calculators is prohibited. WW 1. Determine if the following series converge or diverge, showing clearly how you arrive at your
answer. 0° 2k + 3
(a) Z —3—k— ‘ (20 marks)
k = O
(c) 2 .___._i___
k=2 \/2k(k+ 1)
(d) E 5’13
(e) Z «If—'- (D E k
k=2 «no 2. Determine if the following series converge absolutely or conditionally, or diverge. Show
clearly how you arrive at your answer. (10 marks) (a) >2 (~1)"~’5~
k=0 2k (b) E (—I)k(k’)2 k :1 (2k)!
(C) E cos R k k=1 k
3. Evaluate the following improper integrals. _ (10 marks)
(a) ‘ ~1— dx fa i x 5
w 1 (b) dk 4. Determine the convergence or divergence of the following sequences with the given nth term. If the sequence converges, ﬁnd its limit. (10 marks)
(a) an :nsin (-1 n
_ (n + l)!
(b) a" » n!
(c) a 2 In (n 2)
n n 5. Find the area of the common interior of the circles with polar equations r = 2 case and r = l .
(10 marks) 6. Find the length of the curve given by the polar equation r = a(1 - cos 9), a>0, 0 s 9 s 27:.
(10 marks) 7. Find (a) the distance traveled by a particle traveling on the path of the parametric equation
x = sin 2 t, y = cos 2 t, 0 s t s 7?. and (b) the arc length of the graph of the given parametric equation. (10 marks)
8. Find the area of the surface generated by revolving the graph of x = acos 3 8, y :asin 39, 0 g 8 :3; about the x—axis. (10 marks)
9. Evaluate the following indeﬁnite integral f Sin '1 x dx [or f arcsin x dx]. (10 marks) ...
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This note was uploaded on 01/11/2012 for the course MATH 100 taught by Professor Loveys during the Fall '11 term at McGill.
- Fall '11