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- Let f and g be the functions given by f(x) = 1/4 + sin(πx) amd g(x) = 4
^{-x}. Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of f and g, and let S be the shaded region in the first quadrant enclosed by the graphs of f and g, as shown in the figure above.

(a) Find the area of R.

(b) Find the area of S.

(c) Find the volume of the solid generated when S is revolved about the horizontal line y = -1. - The tide removes sand from Sandy Point Beach at a rate modeled by the function R, given by
- A metal wire of length 8 centimeters (cm) is heated at one end. The table above gives selected values of the temperature T(x), in degrees Celsius (°C), of the wire x cm from the heated end. The function T is decreasing and twice differentiable.
- Let f be a function that is continuous on the interval [0, 4). The function f is twice differentiable except at x = 2. The function f and its derivatives have the properties indicated in the table above, where DNE indicates that the derivatives of f do not exist at 2.
- A car is traveling on a straight road. For 0 24 £ £t seconds, the car’s velocity v t( ), in meters per second, is modeled by the piecewise-linear function defined by the graph above.
- Consider the differential equation

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