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: 6

Answer

$\lim\limits_{x \to 2}f(x) = \infty$ $\lim\limits_{x \to -2+}f(x) = \infty$ $\lim\limits_{x \to -2^-}f(x) = -\infty$ $\lim\limits_{x \to -\infty} f(x) = 0$ $\lim\limits_{x \to \infty} = 0$ $f(0) = 0$

Work Step by Step

$\lim\limits_{x \to 2}f(x) = \infty$ As $x$ approaches $2$ from the left and the right, 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 positive numbers. $\lim\limits_{x \to -2^-}f(x) = -\infty$ As $x$ approaches $-2$ from the left, the value of the function becomes larger magnitude negative numbers. $\lim\limits_{x \to -\infty} f(x) = 0$ As $x$ approaches larger magnitude negative numbers, the value of the function gets closer and closer to 0 $\lim\limits_{x \to \infty} = 0$ As $x$ approaches larger magnitude positive numbers, the value of the function gets closer and closer to 0 $f(0) = 0$
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