Calculus 8th Edition

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

Chapter 13 - Vector Functions - 13.3 Arc Length and Curvature - 13.3 Exercises - Page 908: 29



Work Step by Step

As we are given that $y=xe^x$ Let us consider $f(x)=y=xe^x$ Write formula 11. $\kappa(x)=\dfrac{|f''(x)|}{[1+(f'(x))^2]^{3/2}}$ $f'(x)=e^x+xe^x$ and $f''(x)=e^x(2+x)$ Thus, $\kappa(x)=\dfrac{|e^x(2+x)|}{[1+(1+x)e^x)^2]^{3/2}}$ or, $\kappa(x)=\dfrac{e^x|x+2|}{[1+(xe^x+e^x)^2]^{3/2}}$
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