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The pressure at the point (x, y, z) of a gas is given by P = f(x, y, z) = (x, y) = 40 + 5x2 + 2y2 + 422 The pressure P is in pascals and x, y, and z are in cm. a) Give a vector in the direction that the pressure is increasing most rapidly at the point (2,1, 3). b) Compute the rate of change of the pressure in the direction of the vector u = (1, 2, 2) at the point (2, 1, 3). Give units.

The pressure at the point (x, y, z) of a gas is given by P = f(x, y, z) = (x, y) = 40 + 5x2 + 2y2 + 422 The pressure P is in pascals and x, y, and z are in cm. a) Give a vector in the direction that the pressure is increasing most rapidly at the point (2,1, 3). b) Compute the rate of change of the pressure in the direction of the vector u = (1, 2, 2) at the point (2, 1, 3). Give units.

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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The pressure at the point \((x, y, z)\) of a gas is given by \(P = f(x, y, z) = (x, y) = 40 + 5x^2 + 2y^2 + 4z^2\). The pressure \(P\) is in pascals and \(x, y,\) and \(z\) are in cm. a) Give a vector in the direction that the pressure is increasing most rapidly at the point \((2, 1, 3)\). b) Compute the rate of change of the pressure in the direction of the vector \(\mathbf{v} = (1, 2, 2)\) at the point \((2, 1, 3)\). Give units.
Transcribed Image Text:The pressure at the point \((x, y, z)\) of a gas is given by \(P = f(x, y, z) = (x, y) = 40 + 5x^2 + 2y^2 + 4z^2\). The pressure \(P\) is in pascals and \(x, y,\) and \(z\) are in cm. a) Give a vector in the direction that the pressure is increasing most rapidly at the point \((2, 1, 3)\). b) Compute the rate of change of the pressure in the direction of the vector \(\mathbf{v} = (1, 2, 2)\) at the point \((2, 1, 3)\). Give units.
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