Find the domain and range and describe the level curves for the function f(x,y). f(x, y) = √√4x² - y² O Domain: all points in the xy-plane; range: real numbers 0 ≤ z ≤ 2; level curves: circles with centers at (0,0) and radii r, 0 < r ≤2 Domain: all points in the xy-plane; range: all real numbers; level curves: circles with centers at (0, 0) Domain: all points in the xy-plane satisfying x² + y² = 4; range: real numbers 0 ≤ z ≤ 2; level curves: circles with centers at (0, 0) and radii r, 0 < r ≤ 2 O Domain: all points in the xy-plane satisfying x² + y² ≤ 4; range: real numbers 0 ≤ z ≤ 2; level curves: circles with centers at (0, 0) and radii r, 0 < r ≤ 2
Find the domain and range and describe the level curves for the function f(x,y). f(x, y) = √√4x² - y² O Domain: all points in the xy-plane; range: real numbers 0 ≤ z ≤ 2; level curves: circles with centers at (0,0) and radii r, 0 < r ≤2 Domain: all points in the xy-plane; range: all real numbers; level curves: circles with centers at (0, 0) Domain: all points in the xy-plane satisfying x² + y² = 4; range: real numbers 0 ≤ z ≤ 2; level curves: circles with centers at (0, 0) and radii r, 0 < r ≤ 2 O Domain: all points in the xy-plane satisfying x² + y² ≤ 4; range: real numbers 0 ≤ z ≤ 2; level curves: circles with centers at (0, 0) and radii r, 0 < r ≤ 2
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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Transcribed Image Text:Find the domain and range and describe the level curves for the function f(x,y).
f(x, y) = √√4 - x² - y²
O Domain: all points in the xy-plane; range: real numbers 0 ≤ z ≤ 2; level curves: circles with centers at (0,0) and radii
r₁0 < r ≤2
Domain: all points in the xy-plane; range: all real numbers; level curves: circles with centers at (0, 0)
+
Domain: all points in the xy-plane satisfying y = 4; range: real numbers 0 ≤ z ≤ 2; level curves: circles with
centers at (0, 0) and radii r, 0 < r ≤ 2
○ Domain: all points in the xy-plane satisfying x² + y² ≤ 4; range: real numbers 0 ≤ z ≤ 2; level curves: circles with
centers at (0, 0) and radii r, 0 < r ≤2
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