Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 2: Limits and Continuity - Section 2.2 - Limit of a Function and Limit Laws - Exercises 2.2: 19

Answer

16

Work Step by Step

We know if $f$ is a polynomial function and $a$ is any real number, then $\lim\limits_{x \to a}f(x)=f(a)$. Using this along with the power and root rules for limits, we have $\lim\limits_{y \to -3}(5-y)^{\frac{4}{3}}=(5-(-3))^{\frac{4}{3}}=(5+3)^{\frac{4}{3}}=(8)^{\frac{4}{3}}=(8^{\frac{1}{3}})^4=2^4=16.$
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