Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.2 Limits: A Numerical and Graphical Approach - Exercises - Page 54: 13


See the proof below.

Work Step by Step

We have $$ |x^2-0| = |(x+0)(x-0)| =x|x-0|$$ Since $|x^2 − 0| $ is a multiple of $|x-0|$, then $|x^2 − 0| $ is arbitrarily small whenever $ x $ is close to $0$. Hence, we get $$\lim_{x\rightarrow 0}x^2=0.$$
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