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Suppose f(x, y) = (a) ▼ ƒ(x, y) = (b) Vƒ(4,5) = (c) fu (4, 5) = D„ ƒ(4, 5) = and u is the unit vector in the direction of (2, -1). Then, x² + y²

Suppose f(x, y) = (a) ▼ ƒ(x, y) = (b) Vƒ(4,5) = (c) fu (4, 5) = D„ ƒ(4, 5) = and u is the unit vector in the direction of (2, -1). Then, x² + y²

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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Suppose \( f(x, y) = \frac{4}{x^2 + y^2} \) and \( \mathbf{u} \) is the unit vector in the direction of \(\langle 2, -1 \rangle\). Then, (a) \( \nabla f(x, y) = \) [blank space] (b) \( \nabla f(4, 5) = \) [blank space] (c) \( f_{\mathbf{u}}(4, 5) = D_{\mathbf{u}} f(4, 5) = \) [blank space]
Transcribed Image Text:Suppose \( f(x, y) = \frac{4}{x^2 + y^2} \) and \( \mathbf{u} \) is the unit vector in the direction of \(\langle 2, -1 \rangle\). Then, (a) \( \nabla f(x, y) = \) [blank space] (b) \( \nabla f(4, 5) = \) [blank space] (c) \( f_{\mathbf{u}}(4, 5) = D_{\mathbf{u}} f(4, 5) = \) [blank space]
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