Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 2: Limits and Continuity - Section 2.5 - Continuity - Exercises 2.5 - Page 85: 51


See the graph below.

Work Step by Step

See the graph and table above in which we evaluate $f(x)$ when x is close to 0, on either side of zero. This gives an approximation of the one-sided limits. The function can not be extended to a continuous function, as the left-sided limit at x=0 $(-1)$ does not equal the right-sided limit at x=0 $(1)$. If we set $f(0)=1$ , f will be continuous from the right. If we set $f(0)=-1$ , f will be continuous from the left.
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