2y X in the direction of (1, 2). Then, Suppose f(x, y) (a) ▼ f(x, y) = (b) ▼ ƒ(6, π) = = = sin (c) fu (6, π) = Du ƒ(6, ñ) = and u is the unit vector

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Suppose \( f(x, y) = \sin\left(\frac{2y}{x}\right) \) and \( \mathbf{u} \) is the unit vector in the direction of \(\langle 1, 2 \rangle\). Then,

(a) \( \nabla f(x, y) = \) [ ]

(b) \( \nabla f(6, \pi) = \) [ ]

(c) \( f_{\mathbf{u}}(6, \pi) = D_{\mathbf{u}} f(6, \pi) = \) [ ]
Transcribed Image Text:Suppose \( f(x, y) = \sin\left(\frac{2y}{x}\right) \) and \( \mathbf{u} \) is the unit vector in the direction of \(\langle 1, 2 \rangle\). Then, (a) \( \nabla f(x, y) = \) [ ] (b) \( \nabla f(6, \pi) = \) [ ] (c) \( f_{\mathbf{u}}(6, \pi) = D_{\mathbf{u}} f(6, \pi) = \) [ ]
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