practicetest1.CalcIISPR2008

# practicetest1.CalcIISPR2008 - n = ∞ n =1 √ n 16 √ n...

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Calc II, First Practice Midterm 1. Find the volume of the solid obtained by rotating the region bounded by the given curves about the speci±ed line. Sketch the region, and a typical line in the region you would rotate to obtain a washer or cylinder. (a) y = 1 4 x 2 , y = 5 - x 2 ; about y = - 1 (b) y = e - x 2 , 0 x 1 , y = 0; about y - axis. 2. Determine whether the SEQUENCE converges or diverges. If it converges, ±nd the limit. State the the theorems that you use. (a) a n = [ ln ( n )] 2 n (b) a n = [cos(5 n + e n )] 2 + n 5 1+6 n 5 3. Is this SERIES convergent? If so, what is the sum? Specify which theorems/tests you are using. Σ n = n =1 5 2 n +5 + ( - 1) n 3 n +1 26 n 4. Determine whether the SERIES is convergent or divergent. You may use any of the tests we covered. Specify which theorems/tests you are using. (a) Σ
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Unformatted text preview: n = ∞ n =1 √ n +16 √ n 3-n 2 (b) Σ n = ∞ n =1 e ( n n 2-5 ) (c) Σ n = ∞ n =1 cos( n )+1+16 n 14 n-n 5. Suppose Σ n = ∞ n =1 a n =-1 and s n is the n th partial sum of the series. What is lim n →∞ a n ? What is lim n →∞ s n ? 6. If the n th partial sum of a series Σ n = ∞ n =1 a n is s n = ln ( n + 1), n ≥ 1, ±nd a n , n ≥ 1, and determine if Σ n = ∞ n =1 a n converges. If it does, ±nd the sum. 7. Suppose Σ n = ∞ n =1 a n converges. Does Σ n = ∞ n =1 ( a n + 1 n ) converge? (Hint: If it did converge you could take the di²erence of Σ n = ∞ n =1 ( a n + 1 n ) and Σ n = ∞ n =1 a n and conclude something.)...
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