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AP Calculus Slides April 20, 2007
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AP Calculus Slides April 20, 2007

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Pre-Test on differential equations and an extra practice problem.

Pre-Test on differential equations and an extra practice problem.

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  • 1. (1) The acceleration of a particle moving along the x-axis at any time t ≥ 0 is given by a(t) = 1 + e-t. At t = 0 the velocity of the particle is -2 and its position is 3. The position of the particle at any time t is: (A) (B) (C) (D) (E)
  • 2. (2) Find the average rate of change of y with respect to x on the closed interval [0, 3] if (A) (B) (C) (D) (E)
  • 3. (3) The curve that passes through the point (1, 0) and whose slope at any point (x, y) is equal to has the equation (A) (B) (C) (D) (E)
  • 4. (4) If and y = 2 when , then y = (A) (B) (C) (D) (E)
  • 5. (1) The location of a slow-moving automobile in miles north of the Canada/USA border on highway 75 is given by a function y = ƒ(t), where t represents time in hours since noon yesterday. Suppose that ƒ(1) = 40, that is, the car is 40 miles north of the border at 1:00 pm. The velocity of the car (in miles per hour) depends on both time and location, and is given by the formula: (a) Find the car’s velocity at t = 1. (b) Determine an explicit formula for the location y = ƒ(t). (c) Where is the car at 5:00 pm?
  • 6. (1) The location of a slow-moving automobile in miles north of the Canada/USA border on highway 75 is given by a function y = ƒ(t), where t represents time in hours since noon yesterday. Suppose that ƒ(1) = 40, that is, the car is 40 miles north of the border at 1:00 pm. The velocity of the car (in miles per hour) depends on both time and location, and is given by the formula: (b) Determine an explicit formula for the location y = ƒ(t).
  • 7. (1) The location of a slow-moving automobile in miles north of the Canada/USA border on highway 75 is given by a function y = ƒ(t), where t represents time in hours since noon yesterday. Suppose that ƒ(1) = 40, that is, the car is 40 miles north of the border at 1:00 pm. The velocity of the car (in miles per hour) depends on both time and location, and is given by the formula: (c) Where is the car at 5:00 pm?
  • 8. A population of honeybees grows at an anuual rate equal to 1/4 the number present when there are no more than 10,000 bees. If there are more than 10,000 bees but fewer than 50,000 bees, the growth rate is equal to 1/12 of the number present. If there are 5000 bees now, when will there be 25,000 bees?