Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - Review Exercises - Page 92: 45

Answer

$\lim\limits_{t\to1}h(t)$ does not exist.

Work Step by Step

$\lim\limits_{t\to1^-}h(t)=\lim\limits_{t\to1^-}(t^3+1)=(1^-)^3+1=2.$ $\lim\limits_{t\to1^+}h(t)=\lim\limits_{t\to1^+}(\frac{1}{2}(t+1))=\frac{1}{2}(1^++1)=1.$ Since $\lim\limits_{t\to1^+}h(t)\ne\lim\limits_{t\to1^-}h(t)\to\lim\limits_{t\to1}h(t)$ 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.