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1. Given: f(x,y)== y a. Find and sketch the domain of the given function b. Find and sketch the level curve that passes through (2,-2) c. Find and sketch the gradient at (2,-2) d. Find Duf(2,-2) in the direction of a = 4i – 2j e. Find the equation of the tangent plane to given surface at (2,-2) f. Determine the points on the surface at which the tangent plane is perpenciluar x = 1 + 2t the line: y = 2+t z = 4-t

1. Given: f(x,y)== y a. Find and sketch the domain of the given function b. Find and sketch the level curve that passes through (2,-2) c. Find and sketch the gradient at (2,-2) d. Find Duf(2,-2) in the direction of a = 4i – 2j e. Find the equation of the tangent plane to given surface at (2,-2) f. Determine the points on the surface at which the tangent plane is perpenciluar x = 1 + 2t the line: y = 2+t z = 4-t

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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solve for part e and f

1. Given: f(x, y) = y a. Find and sketch the domain of the given function b. Find and sketch the level curve that passes through (2,-2) c. Find and sketch the gradient at (2,-2) d. Find Duf (2,-2) in the direction of a = 4i - 2j e. Find the equation of the tangent plane to given surface at (2,-2) f. Determine the points on the surface at which the tangent plane is perpenciluar x = 1 + 2t the line: y = 2+t z = 4-t
Transcribed Image Text:1. Given: f(x, y) = y a. Find and sketch the domain of the given function b. Find and sketch the level curve that passes through (2,-2) c. Find and sketch the gradient at (2,-2) d. Find Duf (2,-2) in the direction of a = 4i - 2j e. Find the equation of the tangent plane to given surface at (2,-2) f. Determine the points on the surface at which the tangent plane is perpenciluar x = 1 + 2t the line: y = 2+t z = 4-t
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