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Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector VF(x, y, z).] Surface Point Z = (8, 6, 10) Part 1 of 6 The equation of the surface can be converted to the general form by defining F(x, y, z) as F(x, y, z) = V x2 + y2 – E The gradient of F is the vector given by VF(x, y, z) = Fx(x, y, z)i + F (x, y, z)j + F (х, у, 2)k. Part 2 of 6 Determine the partial derivatives Fx(x, y, z), Fy(x, y, z), and Fz(x, y, z). Falx, Y, z) = (Vx? + y? + y2 F,lx, y, 2) - V + y -2) ду x² + y2 Fe(x, y, 2) = (Vx? + y? - 2) az

Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector VF(x, y, z).] Surface Point Z = (8, 6, 10) Part 1 of 6 The equation of the surface can be converted to the general form by defining F(x, y, z) as F(x, y, z) = V x2 + y2 – E The gradient of F is the vector given by VF(x, y, z) = Fx(x, y, z)i + F (x, y, z)j + F (х, у, 2)k. Part 2 of 6 Determine the partial derivatives Fx(x, y, z), Fy(x, y, z), and Fz(x, y, z). Falx, Y, z) = (Vx? + y? + y2 F,lx, y, 2) - V + y -2) ду x² + y2 Fe(x, y, 2) = (Vx? + y? - 2) az

Calculus: Early Transcendentals
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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Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector VF(x, y, z).] Surface Point z = V x2 + (8, 6, 10) Part 1 of 6 The equation of the surface can be converted to the general form by defining F(x, y, z) as F(x, y, z) = Vx2 + y2 – E The gradient of F is the vector given by VF(x, y, z) = Fx(x, y, z)i + F (x, y, z)j + F (х, у, z)k. Part 2 of 6 Determine the partial derivatives Fx(x, y, z), Fy(x, y, z), and F2(x, y, z). Filx, y, z) = (V + y? - z) x2 FAx, Y, ») = V+yå - 2) ду x² + y2 Fo(X, Y, 2) = (V + y? - 2) az
Transcribed Image Text:Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector VF(x, y, z).] Surface Point z = V x2 + (8, 6, 10) Part 1 of 6 The equation of the surface can be converted to the general form by defining F(x, y, z) as F(x, y, z) = Vx2 + y2 – E The gradient of F is the vector given by VF(x, y, z) = Fx(x, y, z)i + F (x, y, z)j + F (х, у, z)k. Part 2 of 6 Determine the partial derivatives Fx(x, y, z), Fy(x, y, z), and F2(x, y, z). Filx, y, z) = (V + y? - z) x2 FAx, Y, ») = V+yå - 2) ду x² + y2 Fo(X, Y, 2) = (V + y? - 2) az
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