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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)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 4CR
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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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