Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.2 Limits: A Numerical and Graphical Approach - Exercises - Page 54: 32


The limit is not defined.

Work Step by Step

We have to estimate the limit: $\displaystyle\lim_{h\rightarrow 0} \cos\dfrac{1}{h}$ Compute $\cos\dfrac{1}{h}$ for values of $h$ close to 0: $\cos\dfrac{1}{-0.01}\approx 0.86231887$ $\cos\dfrac{1}{-0.001}\approx 0.56237908$ $\cos\dfrac{1}{-0.0001}\approx -0.95215537$ $\cos\dfrac{1}{-0.00001}\approx -0.99936081$ $\cos\dfrac{1}{0.00001}\approx -0.99936081$ $\cos\dfrac{1}{0.0001}\approx -0.95215537$ $\cos\dfrac{1}{0.001}\approx 0.56237908$ $\cos\dfrac{1}{0.01}\approx 0.86231887$ Therefore we got: $\displaystyle\lim_{h\rightarrow 0} \cos\dfrac{1}{h}$ does not exist.
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.