Calculus 8th Edition

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

Chapter 1 - Functions and Limits - 1.5 The Limit of a Function - 1.5 Exercises: 30

Answer

$-\infty$

Work Step by Step

$x\rightarrow 5^{-}$ means that the values of x are positive (close to 5) and being left of 5, slightly less than 5. For any of these x, the numerator is positive and the denominator is negative, as it approaches $0$ from the negative side So, $\displaystyle \lim_{x\rightarrow 5^{-}}\frac{x+1}{x-5}=-\infty$
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