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AP Calculus AB 2006 Free Response Questions - Complete Paper (pdf)

- Let R be the shaded region bounded by the graph of y = ln x and the line y = x - 2, as shown above.

(a) Find the area of R.

(b) Find the volume of the solid generated when R is rotated about the horizontal line y = -3.

(c) Write, but do not evaluate, an integral expression that can be used to find the volume of the solid generated when R is rotated about the y-axis. - At an intersection in Thomasville, Oregon, cars turn left at the rate L(t) = 60√t sin
^{2}(t/3) cars per hour over the time interval 0 18 £ £t hours. The graph of y = L(t) is shown above. - The graph of the function f shown above consists of six line segments.
- Rocket A has positive velocity v t( ) after being launched upward from an initial height of 0 feet at time t = 0 seconds. The velocity of the rocket is recorded for selected values of t over the interval 0 ≤ t ≤ 80 seconds, as shown in the table above.
- Consider the differential equation
- The twice-differentiable function f is defined for all real numbers and satisfies the following conditions:

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