Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter P - P.3 - Functions and Their Graphs - Exercises - Page 29: 82

Answer

The function is even. Zeros: $x=πk$ where k is an integer

Work Step by Step

To check whether a function f is even, odd, or neither, evaluate $f(−x)$. If $f(−x)=f(x)$ then the function is even. If $f(−x)=−f(x)$ then the function is odd. Otherwise the function is neither: $f(x)=\sin^2 x$ $f(−x)=\sin^2 (-x)$ $f(−x)=(-\sin x)^2$ $f(-x)=\sin^2 x$ $f(−x)=f(x)$ Therefore the function is even. The zeros of the function occur whenever $\sin x=0$ So the zeros are $x=πk$ where k is an integer
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