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: 29

Answer

$-\frac{1}{2}$

Work Step by Step

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