Question

) The acceleration due to gravity, g, varies with height above the surface of the earth, in a certain way. If you go down below the surface of the earth, g varies in a different way. It can be shown that g is given by Here R is the radius of the earth, M is the mass of the earth, G is the gravitational constant, and r is the distance to the center of the earth.

Sketch a graph of g against r, and use it to answer the following questions:

A. Is g a continuous function of r? why?


B. Is g a differentiable function of r? why?