Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises: 29

Answer

$A(t)$ is continous on $[-1,0]$.

Work Step by Step

$$A(t)=\arcsin(1+2t)$$ 1) Find the domain of $A(t)$ $\arcsin(1+2t)$ is defined only when $$-1\leq(1+2t)\leq1$$$$-2\leq2t\leq0$$$$-1\leq t\leq0$$ In other words, the domain of $A(t)$ is $t\in[-1,0]$. 2) According to Theorem 7, $A(t)$ is continous on its domain. Therefore, $A(t)$ is continous on $[-1,0]$.
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