University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 2 - Section 2.2 - Limit of a Function and Limit Laws - Exercises - Page 66: 6

Answer

The limit does not exist because $f(x)$ grows too large to have a limit as $x\to1$
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Work Step by Step

$$\lim_{x\to1}\frac{1}{x-1}$$ As $x\to1$, $(x-1)$ approaches $0$, so $\frac{1}{x-1}$ would go infinitely large and does not revolve around any fixed real number. And no, $\infty$ is not accepted as a limit. In other words, the function is not bounded, so its limit does not exist as $x\to 1$. A graph has been enclosed below, showing the graph as $x\to1$.
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