Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.6 Calculating Limits Using the Limit Laws - 1.6 Exercises: 25

Answer

1

Work Step by Step

$\lim\limits_{t \to 0}\frac{\sqrt {1+t}-\sqrt {1-t}}{t}=\lim\limits_{t \to 0}\frac{\sqrt {1+t}-\sqrt {1-t}}{t}*\frac{\sqrt {1+t}+\sqrt {1-t}}{\sqrt {1+t}+\sqrt {1-t}}=\lim\limits_{t \to 0}\frac{1+t-(1-t)}{t(\sqrt {1+t}+\sqrt {1-t})}=\lim\limits_{t \to 0}\frac{2t}{t(\sqrt {1+t}+\sqrt {1-t})}=\lim\limits_{t \to 0}\frac{2}{\sqrt {1+t}+\sqrt {1-t}}=\frac{2}{\sqrt {1+(0)}+\sqrt {1-(0)}}=\frac{2}{2}=1$
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