1. 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, then g varies in a different way. It can be shown that g is always described by: g(x) = GM-x R³ GM if if 0
1. 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, then g varies in a different way. It can be shown that g is always described by: g(x) = GM-x R³ GM if if 0
Transcribed Image Text:1. 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, then g varies in a different way. It can be shown that g is always
described by:
g(x)
=
GM-x
R³
GM
if
if
0<x<R
x>R
where R is the radius of the earth, M is the mass of the earth, G is the gravitational constant, and x is the
distance to the center of the earth.
(a) Sketch a graph of y=g(x) for x≥0. Do not replace the positive constants G, M, R with specific numerical values.
(Notes: Since x is the independent variable, you should measure x along the horizontal axis.
Do not replace the positive constants G, M, and R with specific numerical values.)
(b) Is g continuous at x = R?
Justify your answer by analyzing the one-sided limits of g at x = R and finding the value of g(R).
(c) Compute the piecewise formula for g'(x) and investigate whether or not g is differentiable at
x = R.
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