Calculus 8th Edition

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

Chapter 1 - Functions and Limits - 1.5 The Limit of a Function - 1.5 Exercises: 14

Answer

(a) -1 (b) 1 (c) does not exist

Work Step by Step

$f(x)=\dfrac{x^2+x}{\sqrt {x^3+x^2}}$ First, graph the function (image attached below) (a) As x goes to 0 from the left hand side, y approaches -1. Therefore, $\lim\limits_{x \to 0^-}f(x)=-1$ (b) As x goes to 0 from the right hand side, y approaches 1. Therefore, $\lim\limits_{x \to 0^+}f(x)=1$ (c) $\lim\limits_{x \to 0}f(x)$ does not exist because $\lim\limits_{x \to 0^-}f(x)\ne\lim\limits_{x \to 0^+}f(x)$
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