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2. Consider a function g(x, y, z) = 1 + ln(3x + 6y +9z) and a vector u = (0, -1, 1). (a) Find the directional derivative of g(x, y, z) at the point (-1, 1, 1) in the direction u.

2. Consider a function g(x, y, z) = 1 + ln(3x + 6y +9z) and a vector u = (0, -1, 1). (a) Find the directional derivative of g(x, y, z) at the point (-1, 1, 1) in the direction u.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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2. Consider a function g(x, y, z) = 1 + ln(3x + 6y +92) and a vector u = (0, -1, 1). (a) Find the directional derivative of g(x, y, z) at the point (-1, 1, 1) in the direction u.
Transcribed Image Text:2. Consider a function g(x, y, z) = 1 + ln(3x + 6y +92) and a vector u = (0, -1, 1). (a) Find the directional derivative of g(x, y, z) at the point (-1, 1, 1) in the direction u.
(b) Consider a plane P₁ given by 5x - 2y - 2z = 1. Determine a plane P₂ that is orthogonal to P₁ and intersects P₁ with the line r(t) = (1,2,0) + tu.
Transcribed Image Text:(b) Consider a plane P₁ given by 5x - 2y - 2z = 1. Determine a plane P₂ that is orthogonal to P₁ and intersects P₁ with the line r(t) = (1,2,0) + tu.
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