1. Find the linearization of f(x) = 5/√(1-x) at x = 0.
2. Use differentiation to approximate the maximum error in using 5 cm as the radius of a sphere to calculate its volume if the measurement is off by at most 6 mm. Find the approximation of both the relative and percentage error for the volume.
3. Suppose that fluid is leaking from an overhead pipe and spreading in the shape of a circle on the ground. If the radius of the circle is increasing at a rate of 0.5 feet per minute, how fast is the area of the circle increasing when the radius is 3 feet?
4. A road running north to south crosses a road going east to west at the point P. Car A is driving north along the first road, and car 8 is driving east along the second road. At a particular time car A is 10 kilometers to the north of P and traveling at 50 km/hr, while car 8 is 15 kilometers to the east of P and traveling at 80 km/hr. How fast is the distance between the two cars changing?
5. Find the maximum and minimum values of f(x) = x/x2+25 on [0, 10].