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Consider the function f(x, y) = (e* - 2x) sin(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 (4,4) in the direction in which f decreases most rapidly. vector = (b) Suppose v = 77 +4j+ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4,4). What is a? a =

Consider the function f(x, y) = (e* - 2x) sin(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 (4,4) in the direction in which f decreases most rapidly. vector = (b) Suppose v = 77 +4j+ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4,4). What is a? a =

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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Consider the function f(x, y) = (eª – 2x) sin(y). Suppose S is the surface z = f(x, y). (a) Find a vector which is perpendicular to the level curve of ƒ through the point (4,4) in the direction in which ƒ decreases most rapidly. vector = GI (b) Suppose v = 7i+ 4j + ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4, 4). What is a? a =
Transcribed Image Text:Consider the function f(x, y) = (eª – 2x) sin(y). Suppose S is the surface z = f(x, y). (a) Find a vector which is perpendicular to the level curve of ƒ through the point (4,4) in the direction in which ƒ decreases most rapidly. vector = GI (b) Suppose v = 7i+ 4j + ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4, 4). What is a? a =
You are standing above the point (2, 1) on the surface z = (a) In which direction should you walk to descend fastest? (Give your answer as a unit 2-vector.) direction : = 25 - (x² + 2y²). (b) If you start to move in this direction, what is the slope of your path? slope =
Transcribed Image Text:You are standing above the point (2, 1) on the surface z = (a) In which direction should you walk to descend fastest? (Give your answer as a unit 2-vector.) direction : = 25 - (x² + 2y²). (b) If you start to move in this direction, what is the slope of your path? slope =
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