Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.3 - Calculating Limits Using the Limit Laws - 2.3 Exercises: 11

Answer

$\lim\limits_{x \to 5}\dfrac{x^{2}-6x+5}{x-5}=4$

Work Step by Step

First, apply direct substitution: $\lim\limits_{x \to 5}\dfrac{x^{2}-6x+5}{x-5}=\dfrac{5^{2}-6(5)+5}{5-5}=\dfrac{0}{0}$ $(Indeterminate$ $Form)$ Apply factorization to the numerator: $\lim\limits_{x \to 5}\dfrac{x^{2}-6x+5}{x-5}=\lim\limits_{x \to 5}\dfrac{(x-5)(x-1)}{x-5}=\lim\limits_{x \to 5}x-1=5-1=4$
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