Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.6 Calculating Limits Using the Limit Laws - 1.6 Exercises - Page 70: 13


does not exist

Work Step by Step

$\lim\limits_{x \to 5}\frac{x^2-5x+6}{x-5}=\frac{(5)^2-5(5)+6}{(5)-5}=\frac{0}{0}=$indet so we have to do algebra $\lim\limits_{x \to 5}\frac{x^2-5x+6}{x-5}=\lim\limits_{x \to 5}\frac{(x-3)(x-2)}{(x-5)}$ We can't simplify or do anything further so the limit does not exist.
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