Let a be a real number and f(, y) = 5aa?y + 5æy³. Let v = 3i – j and let Vf(r, y) denote the gradient of f(x, y). i) Find Vf(1,1) in terms of a. -10/5 , find a. ii) If the rate of change of f(r, y) at the point (1, 1) in the direction of v is - v2 O ) (10a + 5) i + (5a + 15) j, i) -2 O i) (10a + 5) i + (5a + 15) j, ii) -6 O i) (10a + 5) i + (5a + 15) j, i) 6 O i) (10a + 5) i + (5a + 15) j, ii) 0 O i) (5a + 5) i + (-10a + 15) j, ii) -2 i) (5a + 5) i + (-10a + 15) j. ii) -6 O i) (5a + 5) i + (-10a + 15) j. ii) 6 i) (5a + 5) i + (-10a + 15) j, i) 0

Q: Let a be a real number and f(x, y) = 3aa?y + 6xy. Let v = 3i – j and let Vf(x, y) denote the…

A:

Q: (a) Find the gradient of f . (b) Evaluate the gradient at the point P. (c) Find the rate of change…

A: The given function f(x,y,z)=xy+yz2+xz3, P(2,0,3)u=-23,-13,23

Q: Consider the following. f(x, y) = ₁ P(9, 1), u = ¹+1 (a) Find the gradient of f. Of(x, y) = (b)…

A: The gradient of f(x, y) is calculated using the formula: ∇f=∂f∂xi+∂f∂yj.

Q: Let a be a real number and f(r, y) = 4az?y+ 8zy". Let v = 3i – j and let Vf(x, y) denote the…

A:

Q: Let a be a real number and f(x, y) = 4ax?y + 8ry³. Let v = 3i – j and let Vf(r, y) denote the…

A:

Q: (- 4,3). a) Let f(x, y)= x²y°. Find the directional derivative of f at P(-1,1) in the direction of ū…

A: a)

Q: Suppose T: R3 M33 is a linear defined by T (x, y, z) = I 2y 0. Then ker(T) is OA. { (0, 0, 0) } Ов.…

A: