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2. A ball is rolling around on a surface with shape given by z = f(x, y) = e-5y sin²x. The ball always rolls in the direction of most rapid decrease of the surface. (a) Calculate the direction in which the ball would roll from a general point (x, y). (b) If the ball's path includes the point (7,√2), calculate the graph of the path y(x).

2. A ball is rolling around on a surface with shape given by z = f(x, y) = e-5y sin²x. The ball always rolls in the direction of most rapid decrease of the surface. (a) Calculate the direction in which the ball would roll from a general point (x, y). (b) If the ball's path includes the point (7,√2), calculate the graph of the path y(x).

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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2. A ball is rolling around on a surface with shape given by z = f(x, y) = e-5y sin²x. The ball always rolls in the direction of most rapid decrease of the surface. (a) Calculate the direction in which the ball would roll from a general point (x, y). (b) If the ball's path includes the point (7,√2), calculate the graph of the path y(x).
Transcribed Image Text:2. A ball is rolling around on a surface with shape given by z = f(x, y) = e-5y sin²x. The ball always rolls in the direction of most rapid decrease of the surface. (a) Calculate the direction in which the ball would roll from a general point (x, y). (b) If the ball's path includes the point (7,√2), calculate the graph of the path y(x).
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