Answer
$-\frac{1}{2}$
Work Step by Step
Given $\lim_{x\to -4}(x\lim_{x\to 0}g(x))=2$, let $\lim_{x\to 0}g(x)=y$, we have $\lim_{x\to -4}(xy)=-4y=2$, which gives $y=-\frac{1}{2}$, thus $\lim_{x\to 0}g(x)=-\frac{1}{2}$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 2: Limits and Continuity - Practice Exercises - Page 100: 6
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