21B-WQ08 - x = e t-t, y = 4 e t/ 2 , ≤ t ≤ 1 . (15 pts)...

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Math 21B Final Exam Please do not turn this page until told to do so. No notes, books, or calculators may be used for this exam. You must show NEAT and COMPLETE work to receive full credit on a problem. Name: Section: SID: Signature: Sections: 001: Deanna, 7:10-8:10 002: Mo, 5:10-6:10 003: Mihaela, 6:10-7:10 004: Josh, 8:10-9:10 Problem(s) Score 1 / 15 2 / 10 3 / 15 4 / 15 5 / 15 6 / 15 7 / 15 Total / 100
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(15 pts) 1. Consider the solid generated by revolving the region bounded on the left by the parabola x = y 2 + 1 and on the right by the line x = 3 about the x -axis. Find the volume of the solid. (10 pts) 2. Find the length of the parametrized curve
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Unformatted text preview: x = e t-t, y = 4 e t/ 2 , ≤ t ≤ 1 . (15 pts) 3. Evaluate the integral i x 2 ln x dx. (15 pts) 4. Evaluate the integral i π/ 2 sin( y ) e cos y dy. (15 pts) 5. Evaluate the integral i x dx x-4 . (15 pts) 6. Evaluate the integral i x dx x 2-3 x + 2 . (15 pts) 7. An alluminum beam was brought from the outside cold into a machine shop where the temperature was held at 65 ◦ F. After 10 min, the beam warmed to 35 ◦ F and after another 10 min it was 50 ◦ F. Find the beam’s initial temperature....
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This note was uploaded on 05/19/2009 for the course MATH 21B taught by Professor Vershynin during the Spring '08 term at UC Davis.

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21B-WQ08 - x = e t-t, y = 4 e t/ 2 , ≤ t ≤ 1 . (15 pts)...

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