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Consider the function f defined by f(x, y) = sin (nxy) + ln(x + y). Do as indicated. (a) In what direction does ƒ have the maximum directional derivative at (x, y) = (0, 1)? (b) Calculate the instantaneous rate of change of f at the point (0, 1, 0) in the direction of the vector A =(4,- 3).

Consider the function f defined by f(x, y) = sin (nxy) + ln(x + y). Do as indicated. (a) In what direction does ƒ have the maximum directional derivative at (x, y) = (0, 1)? (b) Calculate the instantaneous rate of change of f at the point (0, 1, 0) in the direction of the vector A =(4,- 3).

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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Consider the function f defined by f(x, y) = sin (¹xy) + ln(x + y). Do as indicated. (a) In what direction does ƒ have the maximum directional derivative at (x, y) = (0, 1)? (b) Calculate the instantaneous rate of change of f at the point (0, 1, 0) in the direction of the vector A =(4,- 3).
Transcribed Image Text:Consider the function f defined by f(x, y) = sin (¹xy) + ln(x + y). Do as indicated. (a) In what direction does ƒ have the maximum directional derivative at (x, y) = (0, 1)? (b) Calculate the instantaneous rate of change of f at the point (0, 1, 0) in the direction of the vector A =(4,- 3).
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