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: 33


$\displaystyle\lim_{x\rightarrow 0} |x|^x=1$

Work Step by Step

We have to estimate the limit: $\displaystyle\lim_{x\rightarrow 0} |x|^x$ Compute $|x|^x$ for values of $x$ close to 0: $|-0.01|^{-0.01}\approx 1.0471285$ $|-0.001|^{-0.001}\approx 1.0069317$ $|-0.0001|^{-0.0001}\approx 1.0009215$ $|-0.00001|^{-0.00001}\approx 1.0001151$ $|0.00001|^{0.00001}\approx 0.99988488$ $|0.0001|^{0.0001}\approx 0.99907939$ $|0.001|^{0.001}\approx 0.99311605$ $|0.01|^{0.01}\approx 0.95499259$ Therefore we got: $\displaystyle\lim_{x\rightarrow 0} |x|^x=1$
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