Answer
$-\frac{2}{9}$
Work Step by Step
$\lim_{x\to-1}\frac{x^{2/9}-1}{x+1}=f'(x)|_{x=-1}$ where $f(x)=x^{2/9}$ thus we have $f'(x)=\frac{2}{9}x^{-7/9}$ and
$\lim_{x\to-1}\frac{x^{2/9}-1}{x+1}=\frac{2}{9}x^{-7/9}|_{x=-1}=-\frac{2}{9}$
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 3: Derivatives - Section 3.3 Differentiation Rules - Exercises 3.3 - Page 126: 56
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