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1. Use the graph below, consisting of two line segments and a quarter-circle. The graph shows the velocity of an object during a 6-second interval.
For how many values of t in the interval 0 < t < 6 is the acceleration undefined?
2. Use the graph below, consisting of two line segments and a quarter-circle. The graph shows the velocity of an object during a 6-second interval.
During what time interval (in sec) is the speed increasing?
3. If and y = 3 when x = 1, then
4. A solid is cut out of a sphere of radius 2 by two parallel planes each 1 unit fromthe center. The volume of this solid is
5. Which one of the following improper integrals converges?
6. Let f (x) = x5 + 3x - 2, and let f -1 denote the inverse of f. Then (f -1) ′(2) equals
7. Find the domain of the particular solution of = 1 + y2 that passes through the origin.
8. Which of the following statements is (are) true about the graph of y = ln (4 + x2)?
I. It is symmetric to the y-axis.
II. It has a local minimum at x = 0.
III. It has inflection points at x = ±2.