Math 101 Sec S13N01 - Sample Test 3 2013 Question 1 Determine if the following series converge or diverge. State reasons for your conclusions. P∞ arctan(n) P∞ 2π −n P∞ (−1)n+1 √ n−2 n=0 n=0 n=4 P∞ √ n n=1 n3 +1 Math 101 Sec S13N01 - Sample Test 3 2013 P∞ 2n n=1 n! Question 2 A 5-lb monkey is attached to the end of a 30-ft hanging rope that weighs 0.2 lb/ft. The monkey climbs the rope to the top. How much work has it done? Math 101 Sec S13N01 - Sample Test 3 2013 Question 3 Compute the volume generated by revolving x2 + (y − 2)2 = 1 about the x-axis. This yields the volume of a doughnut. Math 101 Sec S13N01 - Sample Test 3 2013 Question 4 Find the arc length of the curve x2/3 + y 2/3 = 4 from x = 1 to x = 8. Math 101 Sec S13N01 - Sample Test 3 2013 Question 5: The fish population in a lake is attacked by a disease at time t = 0, with the result that the size P(t) of the population at time t √ dP = −k P dt where k is a positive constant. If there were initially 90,000 fish in the lake, and 40,000 were left after 6 weeks, when will the fish population be reduced to 10,000? Math 101 Sec S13N01 - Sample Test 3 2013 √ Question 6 Find first five terms of the Maclaurin series for f (x) = x 1 + x2 .

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