The pressure P(x, y) at a point (x, y) = R² on a metal membrane is given by P(x, y) = 100e-x²-2y². Let r = (0, 1). (1) Find the largest increase of pressure at r. (2) What are the directions in which the pressure equals zero.
The pressure P(x, y) at a point (x, y) = R² on a metal membrane is given by P(x, y) = 100e-x²-2y². Let r = (0, 1). (1) Find the largest increase of pressure at r. (2) What are the directions in which the pressure equals zero.
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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Transcribed Image Text:2. The pressure P(x, y) at a point (x, y) = R² on a metal membrane is given
by P(x, y) = 100e-x²-2y². Let r = (0, 1).
(1) Find the largest increase of pressure at r.
(2) What are the directions in which the pressure equals zero.
Expert Solution
Introduction
In this problem, we are given a function P(x,y) that represents the pressure at a point (x,y) on a metal membrane. We are asked to find the largest increase of pressure at a specific point r=(0,1) and the directions in which the pressure equals zero.
We will use the gradient of P to find the direction of largest increase and solve equations to determine the directions in which the pressure does not change.
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