Use the given graph of f(x) = x² to find a number & such that if |x − 1| < & then |x² − 1| < 1/1/1 를 (Round your answer down to three decimal places.) y 8 = 1.5 1 0.5 ? 1 ? y=x² x
Use the given graph of f(x) = x² to find a number & such that if |x − 1| < & then |x² − 1| < 1/1/1 를 (Round your answer down to three decimal places.) y 8 = 1.5 1 0.5 ? 1 ? y=x² x
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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Q3. Please answer the question
![Use the given graph of \( f(x) = x^2 \) to find a number \( \delta \) such that if \( |x - 1| < \delta \), then \( |x^2 - 1| < \frac{1}{2} \).
(Round your answer down to three decimal places.)
**Graph Explanation:**
- The graph shows the function \( y = x^2 \).
- On the \( y \)-axis, markings are labeled at 0.5, 1.0, and 1.5.
- Horizontal lines extend from these points on the \( y \)-axis to the curve and continue vertically down to the \( x \)-axis.
- The significant points of intersection on the \( x \)-axis need to be identified as part of finding \( \delta \).
**Task:** Find \( \delta \) using the visual information and constraints provided by the graph. The goal is to determine the correct \( x \)-values where the vertical distance on the graph stays within \( \frac{1}{2} \).
\[ \delta = \boxed{\text{Enter value here}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b1f7975-4b0c-45ff-85b5-d245674b95f7%2F137f1ffd-32b9-4554-8c1a-2d56f468d7eb%2Fmzm0ici_processed.png&w=3840&q=75)
Transcribed Image Text:Use the given graph of \( f(x) = x^2 \) to find a number \( \delta \) such that if \( |x - 1| < \delta \), then \( |x^2 - 1| < \frac{1}{2} \).
(Round your answer down to three decimal places.)
**Graph Explanation:**
- The graph shows the function \( y = x^2 \).
- On the \( y \)-axis, markings are labeled at 0.5, 1.0, and 1.5.
- Horizontal lines extend from these points on the \( y \)-axis to the curve and continue vertically down to the \( x \)-axis.
- The significant points of intersection on the \( x \)-axis need to be identified as part of finding \( \delta \).
**Task:** Find \( \delta \) using the visual information and constraints provided by the graph. The goal is to determine the correct \( x \)-values where the vertical distance on the graph stays within \( \frac{1}{2} \).
\[ \delta = \boxed{\text{Enter value here}} \]
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