Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 1: Functions - Section 1.1 - Functions and Their Graphs - Exercises 1.1 - Page 12: 35

Answer

Yes, see explanations.

Work Step by Step

If x is an integer, we have $\lceil -x \rceil = -x = -\lfloor x \rfloor $ . If x is not an integer, let M and N be integers (positive or negative) and $ M\lt x \lt N $. Thus, we have $-N\lt -x \lt -M $, so $\lceil -x \rceil = -M $ and $-\lfloor x \rfloor=-M $
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.