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: 26

Answer

-1

Work Step by Step

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