testIIIc1 - the bottom, and the water leaks out at a...

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MATH 1501B1 Test III July 2009 NAME!!! and GTid (9xxxxxxxx): There are 8 questions on this exam on one page (not counting this cover page). Be sure to explain your answers, as answers that are not accompanied by explanations/work may receive no credit. You are to complete this exam completely alone, without the aid of notes, texts, cal- culators, cellular telephones, personal digital assistants, or any other mechanical or digital calculating device. By signing on the line below, you agree to abide by the Georgia Tech Honor Code, the principles of which are embodied by the Challenge Statement: I commit to uphold the ideals of honor and integrity by refusing to betray the trust bestowed upon me as a member of the Georgia Tech community. Student signature: Question Points Score 1 15 2 10 3 15 4 10 5 10 6 10 7 15 8 15 Total: 100
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MATH 1501B1 Test III 16 July 2009 1. (15 points) Calculate R x x + 1 dx 2. (10 points) A rope is used to pull up a bucket of water from the bottom of a 40-foot well. When the bucket is full of water, it weighs 40 pounds; however, there is a hole in
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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 ( x-1) 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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testIIIc1 - the bottom, and the water leaks out at a...

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