Suppose that f: R² → R² is given by f(x, y) = (x³ - 2xy², x+y). Does f has a differentiable local inverse near (1,-1)? If yes, find Df-¹(-1,0) and approximate f-1(-1.5, 0.5).
Suppose that f: R² → R² is given by f(x, y) = (x³ - 2xy², x+y). Does f has a differentiable local inverse near (1,-1)? If yes, find Df-¹(-1,0) and approximate f-1(-1.5, 0.5).
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:Suppose that f: R² → R² is given by f(x, y) = (x³ - 2xy², x+y). Does f has a differentiable local
inverse near (1,-1)? If yes, find Df-¹(-1,0) and approximate f-1(-1.5, 0.5).
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