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If the temperature in a certain room is given by T(x, y, z) = x³ + 2y³ + 3z³ — xyz, what is the rate of change in temperature at (1,1,1) in the (1,2,3) direction. If a particle is floating around along the path p(t) = (t cost +n + 2, t sint + 1, t² − ² + 1), what is the rate of change in temperature experienced by the particle at time t = π?

If the temperature in a certain room is given by T(x, y, z) = x³ + 2y³ + 3z³ — xyz, what is the rate of change in temperature at (1,1,1) in the (1,2,3) direction. If a particle is floating around along the path p(t) = (t cost +n + 2, t sint + 1, t² − ² + 1), what is the rate of change in temperature experienced by the particle at time t = π?

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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If the temperature in a certain room is given by T(x, y, z) = x³ + 2y³ + 3z³ — xyz, what is the rate of change in temperature at (1,1,1) in the (1,2,3) direction. If a particle is floating around along the path p(t) = (t cost +n + 2, t sint + 1, t² − ² + 1), what is the rate of change in temperature experienced by the particle at time t = π?
Transcribed Image Text:If the temperature in a certain room is given by T(x, y, z) = x³ + 2y³ + 3z³ — xyz, what is the rate of change in temperature at (1,1,1) in the (1,2,3) direction. If a particle is floating around along the path p(t) = (t cost +n + 2, t sint + 1, t² − ² + 1), what is the rate of change in temperature experienced by the particle at time t = π?
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