The air temperature (in degrees Celsius) about a point (0, 0, 0) on the Earth surface is given by the function T(x, y, z) = (x² + z²) sin Пху 2 +yz² Suppose P is the point (1, 1, -1). (a) Determine the temperature gradient vector at P. (b) What is the linear approximation to T at P. (c) Determine the tangent plane to T at P. (d) A bird passes through P with speed 5 m.s-¹ in the direction toward point Q = (2,−1, 1). What rate of change of temperature does the bird experience when passing through P?
The air temperature (in degrees Celsius) about a point (0, 0, 0) on the Earth surface is given by the function T(x, y, z) = (x² + z²) sin Пху 2 +yz² Suppose P is the point (1, 1, -1). (a) Determine the temperature gradient vector at P. (b) What is the linear approximation to T at P. (c) Determine the tangent plane to T at P. (d) A bird passes through P with speed 5 m.s-¹ in the direction toward point Q = (2,−1, 1). What rate of change of temperature does the bird experience when passing through P?
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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