Show in each case that f is differentiable at each a =(a, b) E R²:(a) f : R² → R with f(x, y) = x + y°,(b) ƒ : R² → R² with f(x,y)= (x² + y², x² – y²),(c) f : R² → R3 with f(x, y)= (2xy, x² + y², a² – y?).

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Show in each case that f is differentiable at each a = (a,b) E R²: (a) f : R² → R with f(x, y) = x + y³, (b) f : R² → R² with f(x, y) = (x² + y?, x² – y²), (c) f : R² → R³ with f(x, y) = (2xy, x² + y², x² – y²).

Show in each case that f is differentiable at each a = (a,b) E R²: (a) f : R² → R with f(x, y) = x + y³, (b) f : R² → R² with f(x, y) = (x² + y?, x² – y²), (c) f : R² → R³ with f(x, y) = (2xy, x² + y², x² – y²).

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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Show in each case that f is differentiable at each a =
(a, b) E R²:
(a) f : R² → R with f(x, y) = x + y°,
(b) ƒ : R² → R² with f(x,y)
= (x² + y², x² – y²),
(c) f : R² → R3 with f(x, y)
= (2xy, x² + y², a² – y?).

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