Let a be a real number and f(r, y) = 4az?y+ 8zy". Let v = 3i – j and let Vf(x, y) denote the gradient of f(z, y). i) Find Vf(1, 1) in terms of a. -12/5 i) If the rate of change of f(r, y) at the point (1, 1) in the direction of v is V2 find a. O ) (8a + 8) i + (4a + 24) j, i) -3 O ) (8a 8) i + (4a + 24) j, ii) -9 O ) (8a 8) i + (4a + 24) j, i) 9 O ) (8a O ) (4a + 8) i + (-8a - 24) j, i) -3 O ) (4a + 8) i + (4a + 24) j, i1) O 8) i + (-8a + 24)j, i) -9 O i) (4a + 8) i + (-8a - 24) j, i) 9 O i) (4a + 8) i + (-8a - 24) j, i) 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let a be a real number and f(r, y) = 4az?y+ 8zy".
Let v = 3i – j and let Vf(x, y) denote the gradient of f(z, y).
i) Find Vf(1, 1) in terms of a.
-12/5
i) If the rate of change of f(r, y) at the point (1, 1) in the direction of v is
V2
find a.
O ) (8a + 8) i + (4a + 24) j, i) -3
O ) (8a
8) i + (4a + 24) j, ii) -9
8) i + (4a + 24) j, i) 9
+ 8) i + (4a + 24) j, I1) O
O ) (4a + 8) i + (-8a - 24) j, i) -3
O ) (4a + 8) i + (-8a + 24) j, ii) -9
O ) (4a + 8) i + (-8a - 24) j, i) 9
O ) (4a + 8) i + (-8a - 24) j, ii) 0
O ) (8a
O ) (8a
Transcribed Image Text:Let a be a real number and f(r, y) = 4az?y+ 8zy". Let v = 3i – j and let Vf(x, y) denote the gradient of f(z, y). i) Find Vf(1, 1) in terms of a. -12/5 i) If the rate of change of f(r, y) at the point (1, 1) in the direction of v is V2 find a. O ) (8a + 8) i + (4a + 24) j, i) -3 O ) (8a 8) i + (4a + 24) j, ii) -9 8) i + (4a + 24) j, i) 9 + 8) i + (4a + 24) j, I1) O O ) (4a + 8) i + (-8a - 24) j, i) -3 O ) (4a + 8) i + (-8a + 24) j, ii) -9 O ) (4a + 8) i + (-8a - 24) j, i) 9 O ) (4a + 8) i + (-8a - 24) j, ii) 0 O ) (8a O ) (8a
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