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Sketch in the xy - plane the domain of each function : (a) ƒ (x, y) = (√x + √y) · In (x² + y² − 4) - e-ху (b) g(x, y) 2x - Y -1 (c) h (x, y) = sin¯¹ (x) + tan¯¹ (y).

Sketch in the xy - plane the domain of each function : (a) ƒ (x, y) = (√x + √y) · In (x² + y² − 4) - e-ху (b) g(x, y) 2x - Y -1 (c) h (x, y) = sin¯¹ (x) + tan¯¹ (y).

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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Calculus

**1. Sketch in the \(xy\)-plane the domain of each function:** (a) \(f(x, y) = (\sqrt{x} + \sqrt{y}) \cdot \ln(x^2 + y^2 - 4)\) (b) \(g(x, y) = \frac{e^{-xy}}{2x - y}\) (c) \(h(x, y) = \sin^{-1}(x) + \tan^{-1}(y)\) **2. Explain why there is not a level curve for \(f(x, y) = \frac{2 + \sin(xy)}{x^2 + y^2}\) for \(k = -1\).** The image contains mathematical functions for which students are asked to sketch the domain. It also involves an explanation regarding the absence of a certain level curve for a specific function value. There are no graphs or diagrams present, only textual mathematical expressions.
Transcribed Image Text:**1. Sketch in the \(xy\)-plane the domain of each function:** (a) \(f(x, y) = (\sqrt{x} + \sqrt{y}) \cdot \ln(x^2 + y^2 - 4)\) (b) \(g(x, y) = \frac{e^{-xy}}{2x - y}\) (c) \(h(x, y) = \sin^{-1}(x) + \tan^{-1}(y)\) **2. Explain why there is not a level curve for \(f(x, y) = \frac{2 + \sin(xy)}{x^2 + y^2}\) for \(k = -1\).** The image contains mathematical functions for which students are asked to sketch the domain. It also involves an explanation regarding the absence of a certain level curve for a specific function value. There are no graphs or diagrams present, only textual mathematical expressions.
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