Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 4 - Section 4.9 - Antiderivatives - 4.9 Exercises - Page 356: 41

Answer

$f(\theta)=-\sin\theta-\cos\theta+5\theta+4$

Work Step by Step

$ f''(t)=\sin\theta+\cos\theta$ Using the antiderivatives table, $f'(\theta)=-\cos\theta+\sin\theta+C$ Given that $f'(0)=4$ it follows that $4=-1+0+C$ $C=5,$ $f'(\theta)=-\cos\theta+\sin\theta+5$ Using the antiderivatives table, $f(\theta)=-\sin\theta-\cos\theta+5\theta+D$ Given that $f(0)=3$ it follows that $3=-0-1+0+D$ $D=4,$ $f(\theta)=-\sin\theta-\cos\theta+5\theta+4$
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