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Given the surface f(x, y) = -+2 ln y, and the point P = (-1, 3) 4 -) Find the rate of change of fat P in the direction of v = (2, 9). b -- Find all direction vectors for which fdoes not change at P (If there is more than one, describe them parametrically). a -- Provide the equation of a hypersurface G(x, y, z), for which the level surface G(x,y,z) = 0 is identical to the surface z=f(x,y), and find the normal to that level surface. C--

Given the surface f(x, y) = -+2 ln y, and the point P = (-1, 3) 4 -) Find the rate of change of fat P in the direction of v = (2, 9). b -- Find all direction vectors for which fdoes not change at P (If there is more than one, describe them parametrically). a -- Provide the equation of a hypersurface G(x, y, z), for which the level surface G(x,y,z) = 0 is identical to the surface z=f(x,y), and find the normal to that level surface. C--

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Given the surface f(x, y) = a -- -) Find the rate of change of fat P in the direction of v = (2, 9). b-. Find all direction vectors for which f does not change at P (If there is more than one, describe them parametrically). X² +2 ln y, and the point P = (-1, 3) C-- Provide the equation of a hypersurface G(x, y, z), for which the level surface G(x,y,z) = 0 is identical to the surface z=f(x,y), and find the normal to that level surface.
Transcribed Image Text:Given the surface f(x, y) = a -- -) Find the rate of change of fat P in the direction of v = (2, 9). b-. Find all direction vectors for which f does not change at P (If there is more than one, describe them parametrically). X² +2 ln y, and the point P = (-1, 3) C-- Provide the equation of a hypersurface G(x, y, z), for which the level surface G(x,y,z) = 0 is identical to the surface z=f(x,y), and find the normal to that level surface.
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