Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.4 Limits and Continuity - Exercises - Page 68: 86


$f(c)=\displaystyle\lim_{x\rightarrow c} f(x)$

Work Step by Step

A function $f(x)$ has a removable discontinuity if $\displaystyle\lim_{x\rightarrow c} f(x)$ exists, but $\displaystyle\lim_{x\rightarrow c} f(x)\not=f(c)$. The function can be redefined in order to be continuous in $x=c$ in only one way by assigning: $f(c)=\displaystyle\lim_{x\rightarrow c} f(x)$
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