Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.5 Evaluating Limits Algebraically - Exercises - Page 72: 3



Work Step by Step

$ f(-1)=\frac{(-1)^{2}+2(-1)+1}{-1+1}=\frac{0}{0}$ The function has the indeterminate form $\frac{0}{0}$ at x=-1. Transforming algebraically and canceling, we have $\frac{x^{2}+2x+1}{x+1}=\frac{(x+1)(x+1)}{x+1}=x+1$ Evaluating using continuity, we get $\lim\limits_{x \to -1}\frac{x^{2}+2x+1}{x+1}=\lim\limits_{x \to -1}(x+1)=-1+1=0$
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