Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 1 - Limits and Continuity - 1.2 Computing Limits - Exercises Set 1.2 - Page 70: 32


(a) does not exist (b) $1$ (c) $4$

Work Step by Step

Given $$g(t)=\left\{\begin{array}{ll}{t-2,} & {t<0} \\ {t^{2},} & {0 \leq t \leq 2} \\ {2 t,} & {t>2}\end{array}\right.$$ Then (a) Since $\lim_{t\to 0^-}g(t)=\lim_{t\to 0^-}(t-2)=-2 $ and $\lim_{t\to 0^+}g(t)=\lim_{t\to 0^+}(t^2)=0 $, then $\lim_{t\to 0}g(t)$ does not exist (b) Since \begin{align*} \lim_{t\to 1}g(t) &=\lim_{t\to 1}t^2\\ &=1 \end{align*} (c) Since $\lim_{t\to 2^-}g(t)=\lim_{t\to 2^-}(t^2)=4 $ and $\lim_{t\to 2^+}g(t)=\lim_{t\to 2^+}(2t)=4 $, then $\lim_{t\to 2}g(t)=4$
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.