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1. The coefficient of x3 in the Taylor series of ln (1 - x) about x = 0 (the Maclaurin series) is
2. The rate at which a rumor spreads across a campus of college students is given by where P(T) represents the number of students who have heard the rumor after t days. If 200 students heard the rumor today (t = 0), how many will have heard it by midnight the day after tomorrow (t = 2)?
Water is poured at a constant rate into the conical reservoir shown above. If thedepth of the water, h, is graphed as a function of time, the graph is
4. A 26-foot ladder leans against a building so that its foot moves away from the buildingat the rate of 3 feet per second. When the foot of the ladder is 10 feet from thebuilding, the top is moving down at the rate of r feet per second, where r is
5. If then F ′(x) =
The graph above shows an object's acceleration (in ft/sec2). It consists of a quarter-circle and two line segments. If the object was at restat t = 5 seconds, what was its initial velocity?
7. Water is leaking from a tank at the rate of R(t) = 5 arctan gallons per hour, where t is the number of hours since the leak began. How many gallons will leak out duringthe first day?
8. The first-quandrant area inside the rose r = 3 sin 2θ is approximately