Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 10 - Section 10.1 - Limits: Numerical and Graphical Viewpoints - Exercises - Page 699: 31a

Answer

$\displaystyle \lim_{\mathrm{x}\rightarrow-1}f(x)=1$

Work Step by Step

Follow the steps in "Evaluating Limits Graphically" (steps 3-5: one-sided limits, limit at x=a) x=-1 As we trace the graph on either side of x=$-1$ (but not $-1$ itself), the points on the graph approach the point $(-1,1),$ f(x) approaches $-1$ (from either side), so both one-sided limits exist and equal 1, the limit $\displaystyle \lim_{\mathrm{x}\rightarrow-1}f(x)$ exists, and $\displaystyle \lim_{\mathrm{x}\rightarrow-1}f(x)=1$
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