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 67: 31


$\lim\limits_{x \to 1}\frac{x^{-1}-1}{(x-1)} = -1$

Work Step by Step

Simplify: $\frac{x^{-1}-1}{(x-1)} = \frac{(1-x)}{x(x-1)} = -\frac{(x-1)}{x(x-1)} = -\frac{1}{x}$ Now, $\lim\limits_{x \to 1}\frac{x^{-1}-1}{(x-1)} = -\lim\limits_{x \to 1}\frac{1}{x} = -1$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.