ex6_6401 - x(c lim x → R x sin t 2 dt x 3 3 Determine...

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Problem Sheet 6 for 6401 Due Monday 1 December 2008, at the Problem Class. You should hand in solutions to all problems, but only some of them will be marked. 1. Compute the following indefinite integrals: (a) R 1 x 2 4 - x 2 dx ; (b) R 1 4+ x 2 dx ; (c) R x 2 x 2 - 9 dx . 2. Compute the following limits: (a) lim x 0 cos(3 x ) - 1 sin 2 x ; (b) lim x 0 sin(5 x ) - 5 sin x tan
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Unformatted text preview: x ; (c) lim x → R x sin( t 2 ) dt x 3 . 3. Determine whether the following series converge or diverge. If they converge, find their sums. (a) 3 + 3 4 + 3 4 2 + · · · + 3 4 n + ... ; (b) ∑ ∞ n =0 2-n 3 n-4 ; (c) 1-1 + 1-1 + ... ; (d) ∑ ∞ n =1 1 4 n 2-1 . 1...
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