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) Consider the function 2 = f(x, y) = /16 – (x² + y?)². Find the do- %3D main and the range of f(x,y). Hence, sketch the domain of f (x, y).

) Consider the function 2 = f(x, y) = /16 – (x² + y?)². Find the do- %3D main and the range of f(x,y). Hence, sketch the domain of f (x, y).

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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a) Consider the function z = f(x, y) = 16 – (x² + y²)². Find the do- main and the range of f(x, y). Hence, sketch the domain of f(x, y). r + s b) Given w = 3x + y? + z³ where x = y = In t and z = rst². dw Find ds E c) The relationship between E, n, L and g is given by g = Find 4(nL) the maximum percentage error in g due to errors of 1% in n and 0.5% in both E and L. d) Verify that (0,0) is a critical point for f (x, y) = kx² + y² – 4xy, then determine the values of k when (0,0) is i. a saddle point, and ii. a local minimum point.
Transcribed Image Text:a) Consider the function z = f(x, y) = 16 – (x² + y²)². Find the do- main and the range of f(x, y). Hence, sketch the domain of f(x, y). r + s b) Given w = 3x + y? + z³ where x = y = In t and z = rst². dw Find ds E c) The relationship between E, n, L and g is given by g = Find 4(nL) the maximum percentage error in g due to errors of 1% in n and 0.5% in both E and L. d) Verify that (0,0) is a critical point for f (x, y) = kx² + y² – 4xy, then determine the values of k when (0,0) is i. a saddle point, and ii. a local minimum point.
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