Consider the function f(x, y) = (e - 3x) cos(y). Suppose S is the surface z = f(x, y). (a) Find a vector which is perpendicular to the level curve of f through the point (4,6) in the direction in which f decreases most rapidly. vector = (b) Suppose v = 6i + 7j+ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4, 6). What is a? a=
Consider the function f(x, y) = (e - 3x) cos(y). Suppose S is the surface z = f(x, y). (a) Find a vector which is perpendicular to the level curve of f through the point (4,6) in the direction in which f decreases most rapidly. vector = (b) Suppose v = 6i + 7j+ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4, 6). What is a? a=
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:Consider the function f(x, y) = (e² - 3x) cos(y). Suppose S is the surface z = f(x, y).
(a) Find a vector which is perpendicular to the level curve of f through the point (4, 6) in the direction in which f decreases most rapidly.
vector =
(b) Suppose v = 67 + 7 + ak is a vector in 3-space which is tangent to the surface S at the point P lying on the surface above (4, 6). What is a?
9.
a=
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