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3. Consider the function f(x, y, z) = sin(y) - √x² + 2². Find the gradient vector f(x, y, z) at Po = (1,0,0). (b) () Find its directional derivative at Po = (2, 1, 1). (1, 0, 0) in the direction of u = (c) Find the equation of the tangent plane to the surface given by f(x, y, z) = 0 at Po= (1, 0, 0).

3. Consider the function f(x, y, z) = sin(y) - √x² + 2². Find the gradient vector f(x, y, z) at Po = (1,0,0). (b) () Find its directional derivative at Po = (2, 1, 1). (1, 0, 0) in the direction of u = (c) Find the equation of the tangent plane to the surface given by f(x, y, z) = 0 at Po= (1, 0, 0).

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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3. Consider the function f(x, y, 2) = sin(y) - √x² + 2². Find the gradient vector Vf(x, y, z) at Po = (1,0,0). (b) (ins) Find its directional derivative at Po = (2, 1, 1). (1, 0, 0) in the direction of u = (c) Find the equation of the tangent plane to the surface given by f(x, y, z) = 0 at Po= (1,0,0).
Transcribed Image Text:3. Consider the function f(x, y, 2) = sin(y) - √x² + 2². Find the gradient vector Vf(x, y, z) at Po = (1,0,0). (b) (ins) Find its directional derivative at Po = (2, 1, 1). (1, 0, 0) in the direction of u = (c) Find the equation of the tangent plane to the surface given by f(x, y, z) = 0 at Po= (1,0,0).
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