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Explain why the function is differentiable at the given point. f(x, y) = 10 + e Xcos y, (7, 0) The partial derivatives are f,(x, y) = and f,(x, y) = , so fT, 0) = and f(n, 0) = Both f, and f, are continuous functions, so fis differentiable at (r, 0). Find the linearization L(x, y) of f(x, y) at (7, 0). L(x, y) =

Explain why the function is differentiable at the given point. f(x, y) = 10 + e Xcos y, (7, 0) The partial derivatives are f,(x, y) = and f,(x, y) = , so fT, 0) = and f(n, 0) = Both f, and f, are continuous functions, so fis differentiable at (r, 0). Find the linearization L(x, y) of f(x, y) at (7, 0). L(x, y) =

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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Explain why the function is differentiable at the given point. f(x, y) = 10 + eXYcos y, (п, 0) The partial derivatives are fy(x, y) = and f,(x, y) = ,so fi(п, 0) - and fy,(T, 0) Both fy and fy are continuous functions, so f is differentiable at (T, 0). Find the linearization L(x, y) of f(x, y) at (T, 0). L(x, y)
Transcribed Image Text:Explain why the function is differentiable at the given point. f(x, y) = 10 + eXYcos y, (п, 0) The partial derivatives are fy(x, y) = and f,(x, y) = ,so fi(п, 0) - and fy,(T, 0) Both fy and fy are continuous functions, so f is differentiable at (T, 0). Find the linearization L(x, y) of f(x, y) at (T, 0). L(x, y)
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