Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 2 - Section 2.7 - Derivatives and Rates of Change - 2.7 Exercises - Page 150: 25

Answer

The domain is $(-5,5)$ $g(0) = 1$ $g'(0) = 1$ $g'(-2) = 0$ $\lim\limits_{x \to -5^+}g(x) = \infty$ $\lim\limits_{x \to 5^-}g(x) = 3$

Work Step by Step

The domain is $(-5,5)$ $g(0) = 1$ $g'(0) = 1$ The slope at $~~x=0~~$ is $~~1$ $g'(-2) = 0$ The slope at $~~x=-2~~$ is $~~0$ $\lim\limits_{x \to -5^+}g(x) = \infty$ As $x$ approaches $-5$ from the right, the value of the function becomes larger magnitude positive numbers. $\lim\limits_{x \to 5^-}g(x) = 3$ As $x$ approaches $5$ from the left, the value of the function gets closer and closer to $3$
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