## Calculus 10th Edition

Published by Brooks Cole

# Chapter 1 - Limits and Their Properties - 1.2 Exercises: 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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