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AP Calculus AB April 14, 2009
AP Calculus AB April 14, 2009
AP Calculus AB April 14, 2009
AP Calculus AB April 14, 2009
AP Calculus AB April 14, 2009
AP Calculus AB April 14, 2009
AP Calculus AB April 14, 2009
AP Calculus AB April 14, 2009
AP Calculus AB April 14, 2009
AP Calculus AB April 14, 2009
AP Calculus AB April 14, 2009
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AP Calculus AB April 14, 2009

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Differential Equations pre-test.

Differential Equations pre-test.

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  • 1. Differential Equations Pre-Test or traffic at the boarder Vancouver, BC by flickr user Tristen.Pelton
  • 2. 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?
  • 3. 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).
  • 4. 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?
  • 5. If y = 1 when x = 4 find the solution to the differential equation
  • 6. Find a function ƒ(x) which satisfies the equations ƒ(x)ƒ'(x)=x and ƒ(0) = 1.
  • 7. Radium decomposes at a rate proportional to the amount present. Find an expression for the amount R left after t years, if R0 is present initially and c is the negative constant of proportionality.

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