If f(x) = sin(x), which of the functions or theorems describes the average rate of change of f(x) over the interval [0, 2]? O The Mean Value Theorem: Average rate of change is sin(2)-sin(0) 2-0 O The Mean Value Theorem: Average rate of change is cos(2)-cos(0) 2-0 The average value function: Average rate of change is The average value function: Average rate of change is sin(x) dx ² sin(x) dx
If f(x) = sin(x), which of the functions or theorems describes the average rate of change of f(x) over the interval [0, 2]? O The Mean Value Theorem: Average rate of change is sin(2)-sin(0) 2-0 O The Mean Value Theorem: Average rate of change is cos(2)-cos(0) 2-0 The average value function: Average rate of change is The average value function: Average rate of change is sin(x) dx ² sin(x) dx
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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![### Question:
If \( f(x) = \sin(x) \), which of the functions or theorems describes the average rate of change of \( f(x) \) over the interval \([0, 2]\)?
### Options:
- ( ) The Mean Value Theorem: Average rate of change is \(\dfrac{\sin(2) - \sin(0)}{2 - 0}\).
- ( ) The Mean Value Theorem: Average rate of change is \(\dfrac{\cos(2) - \cos(0)}{2 - 0}\).
- ( ) The average value function: Average rate of change is \(\int_{0}^{2} \sin(x) \, dx\).
- ( ) The average value function: Average rate of change is \(\dfrac{1}{2 - 0} \int_{0}^{2} \sin(x) \, dx\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F883933e7-6864-477d-8bb2-712659e12b95%2F3d065273-27d4-4e02-9d9b-20495737190a%2F8m267b_processed.png&w=3840&q=75)
Transcribed Image Text:### Question:
If \( f(x) = \sin(x) \), which of the functions or theorems describes the average rate of change of \( f(x) \) over the interval \([0, 2]\)?
### Options:
- ( ) The Mean Value Theorem: Average rate of change is \(\dfrac{\sin(2) - \sin(0)}{2 - 0}\).
- ( ) The Mean Value Theorem: Average rate of change is \(\dfrac{\cos(2) - \cos(0)}{2 - 0}\).
- ( ) The average value function: Average rate of change is \(\int_{0}^{2} \sin(x) \, dx\).
- ( ) The average value function: Average rate of change is \(\dfrac{1}{2 - 0} \int_{0}^{2} \sin(x) \, dx\).
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