Calculus Homework Due 4-24-14

1. Find the exact global minimum value of f(x)=x+\frac{1}{x} on the domain \{x|x>0\}

2. Find the exact global minimum and maximum values of g(t)=te^{-t} on the domain \{t|t\geq0\}

3. A certain quantity of gas occupies a volume of 20cc at a pressure of 1 atmosphere. The gas expands without the addition of heat, so, for some constant k, its pressure, P, and volume, V, satisfy the equation PV^{1.4}=k. (a) Find the rate of change of pressure with respect to volume. (b) The volume is increasing at 2cc/min when the volume is 30cc. At that moment, is the pressure increasing or decreasing? How fast?

4. (a) A hemispherical bowl of radius 10cm contains water to a depth of hcm. Find the radius of the surface of the water as a function of h. (b) The water level drops at a rate of 0.1 cm per hour. At the what rate is the radius of the water decreasing when the depth is 5 cm?