Use the graphing guidelines to make a complete graph of f. f(x) = sin x-x on (0,2x) Choose the correct graph below. O A OB. OC. OD. A 8-
Use the graphing guidelines to make a complete graph of f. f(x) = sin x-x on (0,2x) Choose the correct graph below. O A OB. OC. OD. A 8-
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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![### Graphing the Function \( f(x) = \sin x - x \) on \([0, 2\pi]\)
**Instructions:**
Use the graphing guidelines to make a complete graph of the function \( f(x) = \sin x - x \) on the interval \([0, 2\pi]\).
**Choose the correct graph below:**
1. **Option A:**
- The graph appears to show a descending curve beginning around \( y = 0 \), decreasing towards negative values, finishing near \( x = 2\pi \).
- It illustrates a clear decreasing trend.
2. **Option B:**
- Similar to Option A, this graph shows a descending curve, however, it seems to dip further into negative \( y \)-values as it approaches \( x = 2\pi \).
3. **Option C:**
- Features an ascending graph starting from \( y \approx 0 \), rising to positive \( y \)-values by the time it reaches \( x = 2\pi \).
- Exhibits a positive growth.
4. **Option D:**
- Depicts an ascending curve that starts from a higher positive \( y \) value and continues upward as \( x \) moves towards \( 2\pi \).
These graphic options present different interpretations of the behavior of the function within the specified range. Analyze the graphs carefully to determine which one accurately reflects the calculated behavior of \( f(x) = \sin x - x \) on the interval \([0, 2\pi]\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe266977e-f1be-47e2-982b-3dc461fce0dc%2F35be788c-d59f-44de-a88d-eb057b6e2c4d%2F148k6ma_processed.png&w=3840&q=75)
Transcribed Image Text:### Graphing the Function \( f(x) = \sin x - x \) on \([0, 2\pi]\)
**Instructions:**
Use the graphing guidelines to make a complete graph of the function \( f(x) = \sin x - x \) on the interval \([0, 2\pi]\).
**Choose the correct graph below:**
1. **Option A:**
- The graph appears to show a descending curve beginning around \( y = 0 \), decreasing towards negative values, finishing near \( x = 2\pi \).
- It illustrates a clear decreasing trend.
2. **Option B:**
- Similar to Option A, this graph shows a descending curve, however, it seems to dip further into negative \( y \)-values as it approaches \( x = 2\pi \).
3. **Option C:**
- Features an ascending graph starting from \( y \approx 0 \), rising to positive \( y \)-values by the time it reaches \( x = 2\pi \).
- Exhibits a positive growth.
4. **Option D:**
- Depicts an ascending curve that starts from a higher positive \( y \) value and continues upward as \( x \) moves towards \( 2\pi \).
These graphic options present different interpretations of the behavior of the function within the specified range. Analyze the graphs carefully to determine which one accurately reflects the calculated behavior of \( f(x) = \sin x - x \) on the interval \([0, 2\pi]\).
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