Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.2 Exercises - Page 56: 43


$\lim\limits_{x \to 0}$$\sqrt[3] x$ = 0 for given epsilon > 0, we choose delta =$(epsilon)^{3}$

Work Step by Step

From only one side values are approaching to the limit so, by definition we can not take the limit but since the domain of function is [0,$\infty$) and it is obvious that 0 is the limit point, So , we can say $\lim\limits_{x \to 0}$$\sqrt[3] x$ = 0. proof using epsilon and delta: |$\sqrt[3] x$| < epsilon whenever |x - 0| < delta so for given epsilon > 0, we choose delta =$(epsilon)^{3}$
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