For the following function f:R3 → R2 x?yz x² – y) f(x,y,z) = {(x2+ y² + z²'1+z² )• x,y, z) # (0,0,0) (0,0), (x, y, z) = (0,0,0) i) Determine if it is continuous at the origin of coordinates ii) Determine if the Jacobi matrix exists at the point (0,0,0) iiI) Determine if the nparcal derivatives of each of the components of the function are continuous at the origin iv) Determine if the function is differentiable at the origin.
For the following function f:R3 → R2 x?yz x² – y) f(x,y,z) = {(x2+ y² + z²'1+z² )• x,y, z) # (0,0,0) (0,0), (x, y, z) = (0,0,0) i) Determine if it is continuous at the origin of coordinates ii) Determine if the Jacobi matrix exists at the point (0,0,0) iiI) Determine if the nparcal derivatives of each of the components of the function are continuous at the origin iv) Determine if the function is differentiable at the origin.
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:For the following function f:R3 → R2
x?yz
f(x, y, z) ={x2 +y² + z?'1+z?
x2 - y
.(x, y, z) # (0,0,0)
(0,0),
(x, y, z) = (0,0,0)
i) Determine if it is continuous at the origin of coordinates
ii) Determine if the Jacobi matrix exists at the point (0,0,0)
ii) Determine if the nparcal derivatives of each of the components
of the function are continuous at the origin
iv) Determine if the function is differentiable at the origin.
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