Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.1 Definition of the Derivative - Exercises - Page 105: 71

Answer

$$0.06\ \text{amperes.}$$

Work Step by Step

Since $v(t)$ is a line with slope $0.5 $, $v^{\prime}(t)=0.5$ volts/s for all $t .$ From the formula, we get: \begin{align*} i(3)&=C v^{\prime}(3)+ (1 / R) v(3)\\ &=0.01(0.5)+(1 / 100)(5.5)\\ &=0.005+0.055\\ &=0.06\ \text{amperes.} \end{align*}
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