Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 5 - Integration - 5.4 Working with Integrals - 5.4 Exercises: 3

Answer

Both $f(x) = x^{12}$ and $f(x) = sin(x^2)$ are even functions.

Work Step by Step

If $f(-x) = f(x)$, then the function is considered even. If $f(-x) = -f(x)$, then the function is considered odd. For $f(x) = x^{12}$, $f(-x) = (-x)^{12} = x^{12}$ Thus, $f(x) = x^{12}$ is an even function. For $f(x) = sin(x^2)$, $f(-x) = sin((-x)^2) = sin(x^2)$ Thus, $f(x) = sin(x^2)$ is an even function.
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