The voltage, V, in volts, in an electrical outlet is given as a function of time, t, seconds, by the function V 150 cos(1207t). (a) Give an expression for the rate of change of voltage with respect to time. (b) Is the rate of change ever zero? Explain. (c) What is the maximum value of the rate of change?
The voltage, V, in volts, in an electrical outlet is given as a function of time, t, seconds, by the function V 150 cos(1207t). (a) Give an expression for the rate of change of voltage with respect to time. (b) Is the rate of change ever zero? Explain. (c) What is the maximum value of the rate of change?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Voltage Function Analysis in an Electrical Circuit**
The voltage, \( V \), in volts, in an electrical outlet is given as a function of time, \( t \), in seconds, by the function:
\[ V = 150 \cos(120\pi t) \]
**Questions for Analysis:**
(a) **Rate of Change Expression:**
Derive an expression for the rate of change of voltage with respect to time.
(b) **Zero Rate of Change:**
Determine if the rate of change is ever zero, and provide an explanation.
(c) **Maximum Rate of Change:**
Identify the maximum value of the rate of change of the voltage.
This exercise requires understanding of calculus and trigonometric functions to analyze the behavior of the voltage in relation to time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3c7298e3-3d00-4a87-b4cb-338ff2975fde%2F38f698cf-6555-4693-876c-47594d7e16f0%2Fr6x8ya_processed.png&w=3840&q=75)
Transcribed Image Text:**Voltage Function Analysis in an Electrical Circuit**
The voltage, \( V \), in volts, in an electrical outlet is given as a function of time, \( t \), in seconds, by the function:
\[ V = 150 \cos(120\pi t) \]
**Questions for Analysis:**
(a) **Rate of Change Expression:**
Derive an expression for the rate of change of voltage with respect to time.
(b) **Zero Rate of Change:**
Determine if the rate of change is ever zero, and provide an explanation.
(c) **Maximum Rate of Change:**
Identify the maximum value of the rate of change of the voltage.
This exercise requires understanding of calculus and trigonometric functions to analyze the behavior of the voltage in relation to time.
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