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 67: 52


$f(x)$ is discontinuous at $x=1$. The graph is right-continuous at $x=1$

Work Step by Step

Given $$ f(x)=\left\{\begin{array}{ll} {x+1} & {\text { for } x<1} \\ {\dfrac{1}{x}} & {\text { for } x \geq 1} \end{array}\right. $$ From the graph, we see that $f(x)$ has a discontinuity at $x=1$. Since $\lim _{x \rightarrow 1+} f(x)=f(1),$ then $f(x)$ is right-continuous at $x=1$.
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