Let a be a real number and f(x, y) 3ar'y+ 5xy3. Let v = 3i –j and let Vf(x, y) denote the gradient of f(x,y). %3D i) Find Vf(1, 1) in terms of a. – 12/5 ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is V2 find a. O i) (6a + 5) i + (3a + 15) j, ii) -4
Let a be a real number and f(x, y) 3ar'y+ 5xy3. Let v = 3i –j and let Vf(x, y) denote the gradient of f(x,y). %3D i) Find Vf(1, 1) in terms of a. – 12/5 ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is V2 find a. O i) (6a + 5) i + (3a + 15) j, ii) -4
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:Let a be a real number and f(x,y) = 3ax²y+ 5xy³.
Let v = 3i – j and let Vf(x, y) denote the gradient of f(x, y).
%3D
i) Find Vf(1, 1) in terms of a.
-12/5
ii) If the rate of change of f(x, y) at the point (1, 1) in the direction of v is
V2
find a.
O i) (6a + 5) i + (3a + 15) j, ii) -4
O i) (6a + 5) i + (3a + 15) j, ii) -12
O i) (6a + 5) i + (3a + 15) j, ii) 12
O i) (6a + 5) i + (3a + 15) j, ii) 0
O i) (3a + 5) i + (-6a + 15) j, ii) -4
O i) (3a + 5) i + (-6a + 15) j, ii) -12
O i) (3a + 5) i + (-6a + 15) j, ii) 12
O i) (3a + 5) i + (-6a + 15) j, ii) 0
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