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Consider the function f(x, y) = (eª — 4x) cos(y). Suppose S is the surface z = f(x, y). (a) Find a vector which is perpendicular to the level curve of f through the point (2, 3) in the direction in which f decreases most rapidly. vector = (b) Suppose = 27 +33 + ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (2, 3). What is a? a =

Consider the function f(x, y) = (eª — 4x) cos(y). Suppose S is the surface z = f(x, y). (a) Find a vector which is perpendicular to the level curve of f through the point (2, 3) in the direction in which f decreases most rapidly. vector = (b) Suppose = 27 +33 + ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (2, 3). What is a? a =

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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Consider the function f(x, y) = (eª — 4x) cos(y). Suppose S is the surface z = f(x,y). (a) Find a vector which is perpendicular to the level curve of f through the point (2, 3) in the direction in which f decreases most rapidly. vector = (b) Suppose 7 = 27 +3j + ak is surface above (2, 3). What is a? a = vector in 3-space which is tangent to the surface S at the point P lying on the
Transcribed Image Text:Consider the function f(x, y) = (eª — 4x) cos(y). Suppose S is the surface z = f(x,y). (a) Find a vector which is perpendicular to the level curve of f through the point (2, 3) in the direction in which f decreases most rapidly. vector = (b) Suppose 7 = 27 +3j + ak is surface above (2, 3). What is a? a = vector in 3-space which is tangent to the surface S at the point P lying on the
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