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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

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

Advanced Engineering Mathematics
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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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
Expert Solution
Step 1

The given function is fx,y=100-x2-y2

The domain is 100-x2-y2≥0

100-x2-y2≥0

Therefore, x2+y2≤100

Rewrite, x2+y2≤102

Domain of the given function is all points in xy plane satisfying x2+y2≤102.

The range of the function is all real number 0≤z≤10.

 

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