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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![### Exercise: Analyzing the Function \( f(x, y) = \sin(x) - \sin(y) \)
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**Problem Description:**
(2) Consider the function \( f(x, y) = \sin(x) - \sin(y) \).
**Tasks:**
(a) Identify all critical points of \( f(x, y) \) within the domain \( |x| < \pi \) and \( |y| < \pi \). Determine the nature of each critical point as either a local minimum, local maximum, or a saddle point.
(b) On the contour map of \( f(x, y) \) provided on the next page, mark these critical points. Indicate the directions in which \( f(x, y) \) is increasing by drawing arrows.](https://content.bartleby.com/qna-images/question/359cec71-3e27-412a-a3dd-e59d98d0b752/320dd541-c8f8-4e55-9f07-d09ea9c01fe3/sqek3ab_thumbnail.png)
Transcribed Image Text:### Exercise: Analyzing the Function \( f(x, y) = \sin(x) - \sin(y) \)
---
**Problem Description:**
(2) Consider the function \( f(x, y) = \sin(x) - \sin(y) \).
**Tasks:**
(a) Identify all critical points of \( f(x, y) \) within the domain \( |x| < \pi \) and \( |y| < \pi \). Determine the nature of each critical point as either a local minimum, local maximum, or a saddle point.
(b) On the contour map of \( f(x, y) \) provided on the next page, mark these critical points. Indicate the directions in which \( f(x, y) \) is increasing by drawing arrows.
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