Find the domain and range and describe the level curves for the function f(x,y). 2 2 f(x,y)=√100-x-y² O A. Domain: all points in the xy-plane Range: real numbers 0 ≤z ≤ 10 Level curves: circles with centers at (0,0) and radii r, 0

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.1: Functions Of Several Variables
Problem 19E
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Find the domain and range and describe the level curves for the function f(x,y).
2
f(x,y)=√100-x²
-
2
O A. Domain: all points in the xy-plane
Range: real numbers 0 ≤z≤ 10
Level curves: circles with centers at (0,0) and radii r, 0 <r≤ 10
B. Domain: all points in the xy-plane
Range: all real numbers
Level curves: circles with centers at (0,0)
OC. Domain: all points in the xy-plane satisfying x² + y
Range: real numbers 0 ≤z ≤ 10
Level curves: circles with centers at (0,0) and radii r, 0<r≤ 10
≤ 100
D. Domain: all points in the xy-plane satisfying x² + y² = 100
Range: real numbers 0 ≤z≤ 10
Level curves: circles with centers at (0,0) and radii r, 0 < r ≤ 10
Transcribed Image Text:Find the domain and range and describe the level curves for the function f(x,y). 2 f(x,y)=√100-x² - 2 O A. Domain: all points in the xy-plane Range: real numbers 0 ≤z≤ 10 Level curves: circles with centers at (0,0) and radii r, 0 <r≤ 10 B. Domain: all points in the xy-plane Range: all real numbers Level curves: circles with centers at (0,0) OC. Domain: all points in the xy-plane satisfying x² + y Range: real numbers 0 ≤z ≤ 10 Level curves: circles with centers at (0,0) and radii r, 0<r≤ 10 ≤ 100 D. Domain: all points in the xy-plane satisfying x² + y² = 100 Range: real numbers 0 ≤z≤ 10 Level curves: circles with centers at (0,0) and radii r, 0 < r ≤ 10
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