Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.8 Continuity - 1.8 Exercises: 11

Answer

The function is continuous $ a = -1.$

Work Step by Step

By theorem 8 we can write $\lim\limits_{x \to -1} (x + 2x^{3})^{4}$ as $(\lim\limits_{x \to -1} (x + 2x^{3}))^{4}$ This is a polynomial so its limit can be evaluated by substitution. Because it is evaluated by substitution, the value of the function at -1 is equal to the value of the limit at -1 which means that it is continuous.
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