(4)
Let v(t) be the velocity in feet per second of a skydiver at the time t seconds, t >= 0. After her chute opens, her velocity satisfies the differential equation dv/dt = -2(v+17), with the initial condition v(0) = -47
a) Use separation of variables to find an expression for v in terms of t where t is measured in seconds.
b) Terminal velocity is defined as lim v(t) (as t approaches infinity). Find the terminal velocity of the skydiver to the nearest foot per second.
C) It is safe to land when here speed is 20 feet per second. At what time t does she reach this speed?
(5)
Let f(x) be the functiond efined by f(x) = cos^2(x) - cos(x) for 0 <= x <= (3%u03C0/2)
a) determine the exact values of the x-intercepts of the graph of f(x)
b) use calculus to determine the intervals on which f(x) is increasing.
c) find the x-values for which the tangent to f(x) is parallel to the horizontal axis.
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