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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![**Problem Statement:**
Find the integral from 0 to 9 of \( f(x) \) with respect to \( x \), given that
\[ f(x) =
\begin{cases}
5 & \text{for } x < 5 \\
x & \text{for } x \geq 5
\end{cases}
\]
**Explanation:**
- **Function Definition**: The function \( f(x) \) is piecewise defined. For values of \( x \) less than 5, \( f(x) \) is constant at 5. For values of \( x \) greater than or equal to 5, \( f(x) \) equals \( x \).
- **Graphical Representation**: Although not explicitly shown, a graph of \( f(x) \) would have a horizontal line at \( y = 5 \) from \( x = 0 \) to \( x = 5 \), and a line with a slope of 1 starting at \( x = 5 \) with a y-intercept also at 5, extending to \( x = 9 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a15759c-8b82-438f-9d6a-36f728df4f17%2F57985b50-395c-4a55-8eb0-e6358d4d0d07%2F9vfecr9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the integral from 0 to 9 of \( f(x) \) with respect to \( x \), given that
\[ f(x) =
\begin{cases}
5 & \text{for } x < 5 \\
x & \text{for } x \geq 5
\end{cases}
\]
**Explanation:**
- **Function Definition**: The function \( f(x) \) is piecewise defined. For values of \( x \) less than 5, \( f(x) \) is constant at 5. For values of \( x \) greater than or equal to 5, \( f(x) \) equals \( x \).
- **Graphical Representation**: Although not explicitly shown, a graph of \( f(x) \) would have a horizontal line at \( y = 5 \) from \( x = 0 \) to \( x = 5 \), and a line with a slope of 1 starting at \( x = 5 \) with a y-intercept also at 5, extending to \( x = 9 \).
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