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2. At what points of R² is the function continuous? (sin(x² + y²) x² + y² f(x, y) = 0, -, if (x, y) = (0,0) if (x, y) = (0,0)

2. At what points of R² is the function continuous? (sin(x² + y²) x² + y² f(x, y) = 0, -, if (x, y) = (0,0) if (x, y) = (0,0)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Continued Function Analysis in \(\mathbb{R}^2\)** **2. At what points of \(\mathbb{R}^2\) is the function continuous?** The given function \( f(x, y) \) is defined piecewise as follows: \[ f(x, y) = \begin{cases} \frac{\sin(x^2 + y^2)}{x^2 + y^2} & \text{if } (x, y) \ne (0, 0) \\ 0 & \text{if } (x, y) = (0, 0) \end{cases} \]
Transcribed Image Text:**Continued Function Analysis in \(\mathbb{R}^2\)** **2. At what points of \(\mathbb{R}^2\) is the function continuous?** The given function \( f(x, y) \) is defined piecewise as follows: \[ f(x, y) = \begin{cases} \frac{\sin(x^2 + y^2)}{x^2 + y^2} & \text{if } (x, y) \ne (0, 0) \\ 0 & \text{if } (x, y) = (0, 0) \end{cases} \]
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