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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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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.
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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