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Unformatted text preview: the bottom, and the water leaks out at a constant rate of 1 2 gallon for each 10 feet that the bucket is raised. Given that the weight of the rope is negligible, how much work is done in lifting the bucket to the top of the well? (Assume that water weighs 8.3 pounds per gallon.) 3. (15 points) Calculate d dx (ln x ) ln x 4. (10 points) Calculate R 3 xe 3 x dx 5. (10 points) Find the numbers which satsify the equation log x 2 = log 3 x 6. (10 points) Calculate R x 2 ( x1) 2 ( x +1) dx 7. (15 points) Let be the region bounded by the curves x = 0, y = 1, y = x . Express the volume obtained by revolving about the line y = 2 by an integral with respect to x and also by an integral with respect to y . (YOU DO NOT HAVE TO EVALUATE THESE INTEGRALS, but if you choose to for your own benet that is ok.) 8. (15 points) Addendum. Page 1 of 1...
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 Fall '08
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