y 4 y = f(x) 3 1 1 2 3 4 Calculate A(1), À(3), A' (1), and A' (3).
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
![**Problem Statement:**
Find formulas for \( A(x) \) on \([0, 2]\) and \((2, 4]\).
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
---
**Attempted Solutions:**
- On \([0, 2]\), \( A(x) = 2x \)
- On \((2, 4]\), \( A(x) = 10x \)
**Feedback:**
- Both solutions are noted as "Incorrect."
---
**Reference:**
The problem is sourced from: Rogawski 4e Calculus Early Transcendentals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0a9522d-164b-4f9a-91f3-55e6c1137254%2F5e61f420-9dfc-4b71-b912-90d690b8bc56%2Fqbjxtc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find formulas for \( A(x) \) on \([0, 2]\) and \((2, 4]\).
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
---
**Attempted Solutions:**
- On \([0, 2]\), \( A(x) = 2x \)
- On \((2, 4]\), \( A(x) = 10x \)
**Feedback:**
- Both solutions are noted as "Incorrect."
---
**Reference:**
The problem is sourced from: Rogawski 4e Calculus Early Transcendentals.
![**Graph Description**
The graph presented is a line graph with the function \( y = f(x) \) displayed. The graph has the following characteristics:
- The x-axis ranges from 0 to 4.
- The y-axis ranges from 1 to 4.
- The graph features a piecewise linear function with a line segment connecting the points \((1, 2)\) and \((4, 4)\).
**Question**
Calculate \( A(1) \), \( A(3) \), \( A'(1) \), and \( A'(3) \).
(Use decimal notation. Give your answers to one decimal place if needed.)
**Answers**
- **\( A(1) \)**: The value is provided as 2.
- **\( A(3) \)**: The calculation is shown as
\[
4 + \frac{2+3}{2}
\]
- **\( A'(1) \)**: The value provided is 0, but it is marked as incorrect.
- **\( A'(3) \)**: There is no provided input or result for this calculation.
**Note**: The question and graph are sourced from "Rogawski 4e: Calculus Early Transcendentals" and published by W.H. Freeman.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0a9522d-164b-4f9a-91f3-55e6c1137254%2F5e61f420-9dfc-4b71-b912-90d690b8bc56%2Fxn54gy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graph Description**
The graph presented is a line graph with the function \( y = f(x) \) displayed. The graph has the following characteristics:
- The x-axis ranges from 0 to 4.
- The y-axis ranges from 1 to 4.
- The graph features a piecewise linear function with a line segment connecting the points \((1, 2)\) and \((4, 4)\).
**Question**
Calculate \( A(1) \), \( A(3) \), \( A'(1) \), and \( A'(3) \).
(Use decimal notation. Give your answers to one decimal place if needed.)
**Answers**
- **\( A(1) \)**: The value is provided as 2.
- **\( A(3) \)**: The calculation is shown as
\[
4 + \frac{2+3}{2}
\]
- **\( A'(1) \)**: The value provided is 0, but it is marked as incorrect.
- **\( A'(3) \)**: There is no provided input or result for this calculation.
**Note**: The question and graph are sourced from "Rogawski 4e: Calculus Early Transcendentals" and published by W.H. Freeman.
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