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AP Calculus AB 2007 Free Response Questions - Complete Paper (pdf)

- Let R be the region in the first and second quadrants bounded above by the graph of
- The amount of water in a storage tank, in gallons, is modeled by a continuous function on the time interval 0 ≤ t ≤ 7, where t is measured in hours. In this model, rates are given as follows:
- The functions f and g are differentiable for all real numbers, and g is strictly increasing. The table above gives values of the functions and their first derivatives at selected values of x. The function h is given by h(x) = f(g(x)) - 6.
- A particle moves along the x-axis with position at time t given by x(t) = e
^{-t}sin t for 0 ≤ t ≤ 2π. - The volume of a spherical hot air balloon expands as the air inside the balloon is heated. The radius of the balloon, in feet, is modeled by a twice-differentiable function r of time t, where t is measured in minutes. For 0 < t < 12, the graph of r is concave down. The table above gives selected values of the rate of change, r'(t), of the radius of the balloon over the time interval 0 ≤ t ≤ 12. The radius of the balloon is 30 feet when t = 5.
- Let f be the function defined by f(x) = k√ - ln x for x > 0, where k is a positive constant.

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