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Over a certain spatial region, suppose that the temperature T is given by T(x,y, z) = 5x2 - 3ry+ xyz %3D Further, assume that a bee is located at the point (3, 4, 5). (a) In which direction should the bee move so that T decreases the fastest? (b) Find the equation of the tangent plane to the level surface T(x,y, z) = T(3, 4, 5) at the point (r, y) = (3, 4). %3D (c) What is the rate of change of the temperature if the bee starts to follow the direction given by any vector from the plane in part(b)?

Over a certain spatial region, suppose that the temperature T is given by T(x,y, z) = 5x2 - 3ry+ xyz %3D Further, assume that a bee is located at the point (3, 4, 5). (a) In which direction should the bee move so that T decreases the fastest? (b) Find the equation of the tangent plane to the level surface T(x,y, z) = T(3, 4, 5) at the point (r, y) = (3, 4). %3D (c) What is the rate of change of the temperature if the bee starts to follow the direction given by any vector from the plane in part(b)?

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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дхду ду? Q3. Over a certain spatial region, suppose that the temperature T is given by T(x,y, z) = 5x² - 3ry+ xyz Further, assume that a bee is located at the point (3,4,5). (a) In which direction should the bee move so that T decreases the fastest? (b) Find the equation of the tangent plane to the level surface T(x, y, z) = T(3,4, 5) at the point (x, y) = (3, 4). (c) What is the rate of change of the temperature if the bee starts to follow the direction given by any vector from the plane in part(b)? 1 ch Live 100%
Transcribed Image Text:дхду ду? Q3. Over a certain spatial region, suppose that the temperature T is given by T(x,y, z) = 5x² - 3ry+ xyz Further, assume that a bee is located at the point (3,4,5). (a) In which direction should the bee move so that T decreases the fastest? (b) Find the equation of the tangent plane to the level surface T(x, y, z) = T(3,4, 5) at the point (x, y) = (3, 4). (c) What is the rate of change of the temperature if the bee starts to follow the direction given by any vector from the plane in part(b)? 1 ch Live 100%
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