Calculus: Early Transcendentals 9th Edition

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

Chapter 2 - Section 2.5 - Continuity - 2.5 Exercises - Page 126: 68

Answer

(a) Prove Theorem 4, part 3 $\lim\limits_{x \to a}$$f(x)$ $=$ $f(a)$ $c$$\lim\limits_{x\to a}$$f(x)$ $=$ $c$$f(a)$ $\lim\limits_{x \to a}$$c$$f(x)$ $=$ $c$$f(a)$ $Proved$ $(b)$ $Prove$ $Theorem 4$ $,$ $part5$ $\lim\limits_{x \to a}$ $\frac{f(x)}{g(x)}$ $=$ $\frac{\lim\limits_{x \to a}f(x)}{\lim\limits_{x \to a} g(x)}$ $=$ $\frac{f(a)}{g(a)}$ $=$ $\frac{f}{g}$$(a)$ $Proved$

Work Step by Step

$(a)$ $Prove$ $Theorem 4$ $,$ $part3$ $\lim\limits_{x \to a}$$f(x)$ $=$ $f(a)$ $c$$\lim\limits_{x\to a}$$f(x)$ $=$ $c$$f(a)$ $\lim\limits_{x \to a}$$c$$f(x)$ $=$ $c$$f(a)$ $Proved$ $(b)$ $Prove$ $Theorem 4$ $,$ $part5$ $\lim\limits_{x \to a}$ $\frac{f(x)}{g(x)}$ $=$ $\frac{\lim\limits_{x \to a}f(x)}{\lim\limits_{x \to a} g(x)}$ $=$ $\frac{f(a)}{g(a)}$ $=$ $\frac{f}{g}$$(a)$ $Proved$
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