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Unformatted text preview: Chapter 6 Test
x December 10, 2002
cos 2 x dx. Name 1. Evaluate
1 e2 2. Evaluate 2x
0 18 1
3 dx. 3. Solve the initial value problem. Support your answer by overlaying your solution on a slope field for the differential equation. dy 3 x2 2x 2 y0 1 dx
3 2 1 -2 -1 1 2 -1
6 4. Evaluate
2 1 sin2 x dx. 5. Use separation of variables to solve the following differential equation : dy dx 4 y ln x x ye 1. 6. Evaluate e3 x cos
3 x x 2 dx. 7. Evaluate e dx. 8. Evaluate cot2 x sec x dx. x2 ln x dx. 9. Evaluate 10. The relative growth rate of the population of the state of South Dakota is 0.1 and its current population is P0 500000. When will the population reach 1 million people ? 11. The population of students at Monta Vista High School is represented by dP 1 1 the logistic differential equation P P2 , where t is dt 2 6000 measured in years a Find k and the carrying capacity, M, for the population b The initial population is P 0 2000 students. Find a formula for the population in terms of t. 12. The temperature of a plate is 80 °C as it is taken out of the oven. The temperature of the room is 30 °C, and after 40 minutes the plate cools to 60 °C. How long will it take for the plate to cool to 50 °C ? 13. Mr. DeRuiter is riding his bike, and together he and the bike have a mass of 90 kilograms. His initial velocity is 10 m sec. The bike s motion obeys the equation v v0 e k m t with k 2 kg sec a Find about how far the bike will coast before reaching a complete stop b About how long will it take the bike s speed to drop to 5 m sec ? 14. Use Euler s Method to numerically solve the initial value problem y x2 2 y, y1 2, on the interval 1 x 4 starting at x0 1 with dx 1. ...
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