Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 14 - Section 14.5 - The Chain Rule. - 14.5 Exercise - Page 993: 48

Answer

$4.65 Hz/s$ and $576.6$ Hz

Work Step by Step

Use the formula given in the problem. Perceived frequency $=\dfrac{332+34}{332-40} \times 460=576.6$ Hz Now, we have: $\dfrac{d}{dt}[\dfrac{C+V_0}{C-f_s}f] =\dfrac{(C-f_s)(C+V_0)'-(C+V_0)(C-V_s)}{(C-f_s)^2}f$ Re-write as: $\dfrac{d}{dt}[\dfrac{C+V_0}{C-f_s}f] =\dfrac{(C-f_s)(V_0)'+(C+V_0)(V_s)}{(C-f_s)^2}f$ Plug in the given values: $\dfrac{(332-40)(1.2)+(332+34)(1.4)}{(332-40)^2} \times 460=4.65 Hz/s$ Hence, $4.65 Hz/s$ and $576.6$ Hz
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