Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 5 - Applications Of The Definite Integral In Geometry, Science, And Engineering - 5.4 Length Of A Plane Curve - Exercises Set 5.4: 9

Answer

False.

Work Step by Step

A smooth curve must have a derivative that is continuous on an interval $[a,b]$. The derivative of $y$ is $$\frac{-2x}{\sqrt{1-x^{2}}}$$ This has an asymptote at both $x=1$ and $x=-1$, so the derivative cannot be continuous on $[-1,1]$ and the graph is not smooth.
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