Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 1 - Limits and Continuity - 1.2 Computing Limits - Exercises Set 1.2: 49

Answer

$\lim\limits_{r \to 0^{+}}F(r)$ = +$\infty$

Work Step by Step

According to Newton’s Law of Universal Gravitation: F(r) = G$\frac{Mm}{r²}$, where r is the distance between the centers of the masses. G, M and m are constants. So as they get closer and closer together, $r\to0$: $\lim\limits_{r \to 0^{+}}F(r)$ = $\lim\limits_{r \to 0^{+}}G\frac{Mm}{r²}$ = +$\infty$. That means the force increases becoming very large. Of course, r is the distance between the centers of the masses, so the distance can't be 0. In a distance r $\gt$ 0 the masses will be touching each other.
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