I have a test tomorrow in my calc class and have a few problems I'm having trouble with after going through the chapter review problems. So any help and explaination would be great, thanks.
1) Find the linearization of f(x) = (1+3x)^(1/3) at a = 0. State the corresponding linear approximation and use it to give an approximate value for (1.03)^(1/3)
2) The volume of a cube is increasing at a rate of 10cm^3/min. How fast is the surface area increasing when the length of an edge is 30cm?
3) An oil tanker runs aground and ruptures. Suppose the leaking oil spreads out in a cicle centered at the tanker and the area of that circle increases at a constate rate at five square miles per hour. Compute the rate of change of the radius of the oil spill at hte moment when the radius is four miles.
Thanks again for any help.