math12 - ∞ X n =1 n n 4 1 8 Test the following series for...

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Practice Exam for midterm II 1. A large tank is designed with ends in the shape of the region between the curves y = 1 2 x 2 and y = 12, measured in feet. Find the hydrostatic force on one end of the tank if it is ﬁlled to a depth of 8 ft with gasoline. (Assume the gasoline’s density is 42 . 0 lb/ft 3 .) 2. Calculate the moments M x , M y and the center of mass of the region bounded by x 2 + y 2 = 9 in the ﬁrst quadrant. 3. Find a formula for the general term a n of the sequence { 1 e 2 , - 4 e 3 , 9 e 4 , - 16 e 5 , · · · } Then evaluate the limit of this sequence. 4. Use the integral test to determine whether the series is convergent or divergent: X n =1 1 8 n + 1 5. Determine whether the series is convergent or divergent. If it is convergent, ﬁnd its sum: X n =1 2 n 2 + 3 n + 2 6. Express the number as a ratio of integers: 3 . ¯ 2 = 3 . 2222 · · · 7. Test whether the series is convergent or divergent:
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Unformatted text preview: ∞ X n =1 n n 4 + 1 8. Test the following series for convergence or divergence. Then give an estimate of | R 10 | = | S-S 10 | . 7 ln 2-7 ln 3 + 7 ln 4-7 ln 5 + 7 ln 6- · · · 9. Determine whether ∑ ∞ n =1 sin(4 n ) 4 n is absolutely convergent, conditionally convergent, or diver-gent. 10. Determine whether ∑ ∞ n =1 ± n 2 +1 2 n 2 +1 ² n is absolutely convergent, conditionally convergent, or divergent. 11. Determine whether the series ∑ ∞ n =1 (-1) n +1 4 √ n is absolutely convergent, conditionally convergent, or divergent. 12. Determine whether the series ∑ ∞ n =1 n ! 100 n is absolutely convergent, conditionally convergent, or divergent. 1...
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This note was uploaded on 09/22/2011 for the course MATH 2153 taught by Professor Staff during the Fall '08 term at Oklahoma State.

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