Estimate the average value of the function between x = 0 and x = 7. 3 لیا 2 1 N - 1 2 3 The average value is i 4 5 Round your answer to the nearest integer. 6 7 f(x) 8
Estimate the average value of the function between x = 0 and x = 7. 3 لیا 2 1 N - 1 2 3 The average value is i 4 5 Round your answer to the nearest integer. 6 7 f(x) 8
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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![**Title: Estimating the Average Value of a Function**
**Objective:**
Learn how to estimate the average value of a function over a specified interval using a graph.
**Problem Statement:**
Estimate the average value of the function \( f(x) \) between \( x = 0 \) and \( x = 7 \).
**Graph Explanation:**
- The graph displays a curve representing the function \( f(x) \).
- The x-axis is labeled from 0 to 7.
- The y-axis has values ranging from 1 to 4.
- The curve begins at approximately 1 on the y-axis when \( x = 0 \) and rises to a peak slightly above 4 around \( x = 2 \).
- It then gradually decreases towards 3 as \( x \) approaches 7.
**Calculation Instructions:**
1. **Identify Key Points:**
- Note the height of the curve at different values of \( x \) to understand the function's behavior.
2. **Average Value Formula:**
- Use the formula for the average value of a continuous function \( f(x) \) over the interval \([a, b]\):
\[
\text{Average value} = \frac{1}{b-a} \int_{a}^{b} f(x) \, dx
\]
3. **Estimate Area Under Curve:**
- Visually approximate the integral or area under the curve from \( x = 0 \) to \( x = 7 \).
4. **Compute Average Value:**
- Divide the total area by the interval length (7 - 0 = 7).
5. **Round Your Answer:**
- Round the computed average value to the nearest integer.
**Answer Box:**
- "The average value is [ ] ."
- Fill in the box with the rounded integer value of the average.
By following these steps, you can efficiently estimate the average value of the function over the designated interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f1362b4-80e9-4fad-af46-6657807adc71%2F1f9fc593-8288-4d35-ac75-81ba23dc7bd7%2Fd012ula_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Estimating the Average Value of a Function**
**Objective:**
Learn how to estimate the average value of a function over a specified interval using a graph.
**Problem Statement:**
Estimate the average value of the function \( f(x) \) between \( x = 0 \) and \( x = 7 \).
**Graph Explanation:**
- The graph displays a curve representing the function \( f(x) \).
- The x-axis is labeled from 0 to 7.
- The y-axis has values ranging from 1 to 4.
- The curve begins at approximately 1 on the y-axis when \( x = 0 \) and rises to a peak slightly above 4 around \( x = 2 \).
- It then gradually decreases towards 3 as \( x \) approaches 7.
**Calculation Instructions:**
1. **Identify Key Points:**
- Note the height of the curve at different values of \( x \) to understand the function's behavior.
2. **Average Value Formula:**
- Use the formula for the average value of a continuous function \( f(x) \) over the interval \([a, b]\):
\[
\text{Average value} = \frac{1}{b-a} \int_{a}^{b} f(x) \, dx
\]
3. **Estimate Area Under Curve:**
- Visually approximate the integral or area under the curve from \( x = 0 \) to \( x = 7 \).
4. **Compute Average Value:**
- Divide the total area by the interval length (7 - 0 = 7).
5. **Round Your Answer:**
- Round the computed average value to the nearest integer.
**Answer Box:**
- "The average value is [ ] ."
- Fill in the box with the rounded integer value of the average.
By following these steps, you can efficiently estimate the average value of the function over the designated interval.
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