Question 1. Consider the following function: a) Graph the function 3 2 0 ) = { $ 1-2 f(x)= 0≤x≤2 (8-21, 2
Question 1. Consider the following function: a) Graph the function 3 2 0 ) = { $ 1-2 f(x)= 0≤x≤2 (8-21, 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Question 1.** Consider the following function:
\[ f(x) =
\begin{cases}
4, & \text{for } 0 \leq x \leq 2 \\
8 - 2x, & \text{for } 2 < x \leq 4
\end{cases}
\]
a) Graph the function
*Graph explanation:* The graph consists of two parts. The first part is a horizontal line at \( f(x) = 4 \) from \( x = 0 \) to \( x = 2 \). The second part is a linear segment where \( f(x) = 8 - 2x \) which is a line with a negative slope starting from the point where the first part ends. This line decreases from \( x = 2 \) to \( x = 4 \).
b) Compute the left, right, and midpoint Riemann Sums with \( n = 4 \) rectangles.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e440afb-2130-4dde-bd2e-442d345d8394%2F9a9b71d5-6066-4e42-ba43-71e5603d934c%2F1qn9p18_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 1.** Consider the following function:
\[ f(x) =
\begin{cases}
4, & \text{for } 0 \leq x \leq 2 \\
8 - 2x, & \text{for } 2 < x \leq 4
\end{cases}
\]
a) Graph the function
*Graph explanation:* The graph consists of two parts. The first part is a horizontal line at \( f(x) = 4 \) from \( x = 0 \) to \( x = 2 \). The second part is a linear segment where \( f(x) = 8 - 2x \) which is a line with a negative slope starting from the point where the first part ends. This line decreases from \( x = 2 \) to \( x = 4 \).
b) Compute the left, right, and midpoint Riemann Sums with \( n = 4 \) rectangles.
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