Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Section 2.6 - Limits at Infinity; Horizontal Asymptotes - 2.6 Exercises - Page 137: 8

Answer

$\lim\limits_{x \to 2^-}f(x) = \infty$ $\lim\limits_{x \to 2+}f(x) = -\infty$ $\lim\limits_{x \to \infty} = 3$ $f$ is odd

Work Step by Step

$\lim\limits_{x \to 2^-}f(x) = \infty$ As $x$ approaches $2$ from the left, the value of the function becomes larger magnitude positive numbers. $\lim\limits_{x \to 2+}f(x) = -\infty$ As $x$ approaches $2$ from the right, the value of the function becomes larger magnitude negative numbers. $\lim\limits_{x \to \infty} = 3$ As $x$ approaches larger magnitude positive numbers, the value of the function gets closer and closer to 3 $f$ is odd That is, $f(-x) = -f(x)$ for all values of $x$ The graph is symmetric about the origin.
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