s15 - equal intervals. Arrange the numbers I , L 10 , R 10...

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Mathematics 115b Mid-term # 1 2/19/08 Name: Section: Please answer all SIX questions; each question is worth TEN points. You may use the table of integrals supplied with the test. However, books, notes, calculators, computers, cellphones may NOT be used. 1 2 3 4 5 6 Total (1) Find the derivative of Z 2 x tan x t 2 + 1 dt
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(2) Rotate the region bounded by x = y 2 and x = 1 about the line y = 3. Find the volume of the resulting solid. (3) Evaluate Z dx x 2 + 1 - x 2 - 3
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(4) Let L 10 , R 10 , M 10 , T 10 be the approximations to the integral I = Z 2 1 1 /x dx given by the left and right endpoint rules, the midpoint rule and the trapezoidal rule, with 10
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Unformatted text preview: equal intervals. Arrange the numbers I , L 10 , R 10 , M 10 , T 10 in ascending order. [You dont need to calculate numerical values, but a sketch may be helpful.] (5) Is the improper integral Z dx x 2 + 3 x + 2 convergent or divergent? You should give reasons, but you dont have to evaluate the integral. (6) Calculate the integral Z ( 2-1)-1 x + 1 sin x + 1 dx...
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s15 - equal intervals. Arrange the numbers I , L 10 , R 10...

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