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Let U be an open subset of R2 and suppose f: U R has the property that the partial derivatives fx and fy exist for (x, y) = U and are continuous at the point (xo, yo). Then f((xo, Yo) + (u₁, U₂)) = f(xo, Yo) + fx (xo, Yo)U₁ + fy (xo, Yo)u₂ + o(u)

Let U be an open subset of R2 and suppose f: U R has the property that the partial derivatives fx and fy exist for (x, y) = U and are continuous at the point (xo, yo). Then f((xo, Yo) + (u₁, U₂)) = f(xo, Yo) + fx (xo, Yo)U₁ + fy (xo, Yo)u₂ + o(u)

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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Let U be an open subset of R2 and suppose f: U → R has the property that the partial derivatives fx and fy exist for (x, y) = U and are continuous at the point (xo, yo). Then f((xo, Yo) + (U₁, U₂)) = f (xo, Yo) + fx (xo, Yo)U₁ + fy(xo, Yo)u₂ + o(u)
Transcribed Image Text:Let U be an open subset of R2 and suppose f: U → R has the property that the partial derivatives fx and fy exist for (x, y) = U and are continuous at the point (xo, yo). Then f((xo, Yo) + (U₁, U₂)) = f (xo, Yo) + fx (xo, Yo)U₁ + fy(xo, Yo)u₂ + o(u)
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