Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises - Page 125: 44


$F$ is a continuous function of $r$.

Work Step by Step

Using the functions of the problem: $\lim\limits_{r \to R^{-}} F(r) = \frac{GM(R)}{R^{3}} = \frac{GM}{R^{2}}$ $\lim\limits_{r \to R^{+}} F(r) = \frac{GM}{r^{2}} = \frac{GM}{R^{2}}$ Both limits as they approach $R$ from the left and right side are equal, so that means that $\lim\limits_{r \to R} F(r) = \frac{GM}{R^{2}}$ is continuous.
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