Let a be a real number and f(x, y) = 2ax²y + 5æy³. Let v = 3i – jand let Vf(x, y) denote the gradient of f(x, y). i) Find Vf(1, 1) in terms of a.

Q: 7. Given the function f(x, y, z) = x² + y² + z² + xy + xz, find the gradient at P(1,2,1).

A: Must Know : Gradient function is given by ∇f=∂f∂xi+∂f∂yj+∂f∂zkGiven : f(x,y,z)=x2+y2+z2+xy+xz…

Q: Let f be a function defined in R2 by f(x,y) = 3x2 - 2x3 - 3y2 + 6xy.  Find the gradient vector in…

A: We have to solve given problem:

Q: Calculate the gradient Vf, where f (x, y) = In(x² + y²).

A: Given:- f(x,y)=lnx2+y2 To find:- Gradient of f ∇f

Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) %3D Vf(4, 2) =

A: If f is a function of x and y then gradient of f is given by ∇f=∂f∂xi^+∂f∂yj^So, ∇fa,b is given by…

Q: Find the gradient of f(x,y,z) = (x² + y² + z²) 23 26 Vf|(-2,2,-1) = i+ 23 54 |j+ 54 27 (Type…

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Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vf|(−2,2,− 1) = ₁ + Oj + k (Type integers or…

A: We want to find the gradient of the given function at point (-2,2,-1).

Q: Find the gradient of the function f(x,y,z) = x2 + y3 - 2z + z In x at point P (2, 2,1) %3D

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y2 +6, (3, 1) Vf(3, 1) = 2i+…

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Q: If F = xi + -4yj +x2k determine the flux of F through S, where S is the portion of z2 = x2 + y2,…

A: Given - F = x i^ - 4y j^ + x2 k^  ;             S is the portion of z2 = x2 +y2 , 1 ≤ z ≤ 3 To find…

Q: Find the gradient of f(x,y.z)= (x2 + y2 + z2) - 1/2 + In (xyz) at the point (1,- 2, - 2) %3D Vf (1.…

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Q: Calculate the gradient of h(x, y, z) = ÷ 1, Vh <-1/(x^2y)z,-1/(xy^2)z, 1/(xy):

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Q: Compute the gradient of the function at the given point. f (x, y, z) = In(x² + 7y - 3z²), (7,7, 7)…

A: option (b) is correct

Q: Let a be a real number and f(x, y) = 5ax²y+ 4xy³. Let v = 3i – j and let Vf(x, y) denote the…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Find the gradient of f(r, y, z) = xy?z³ + In(ryz) at the point (1, 1, 1).

A:

Q: Find the gradient of f(x, y, z) =e^y cos(xz) at (1,0,1) .

A:

Q: Find the gradient of the function f(x, y) = x²y+y³. Vf(x, y) = xî+ (x + 3y²) ĵ ○ ▼ f(x, y) = xyî +…

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Q: Let a be a real number and f(x, y) = 5ax?y+ 5xy³. Let v = 3i – j and let Vf(x, y) denote the…

A:

Q: Find the gradient of following scalar function: |5x+7y'•3z r = V

A: Gradient of any function r=f(x,y,z) is given by the formula ∇r=∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z Where…

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 5y + 4, (3, 2) %3D Vf(3, 2) =

A: We will solve the problem.

Q: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: ○ (2x,-1,-1/2) (2x₂ O…

A:

Q: Let a be a real number and f(x, y) = 4ax²y+ 8xy³. Let v = 3i – j and let Vf(x, y) denote the…

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Q: Find the gradient of f(x,y,z) = (x² + y² +z²) Vf|(1,2,2) = Oi+Dj+Ok (Type integers or simplified…

A: ∇f(x,y,z) = ∂∂xi+∂∂yj+∂∂zkf(x,y,z)

Q: Let F1 = (x+ y)Âx + (-x+y) ŷ– 2zî and F2 = 2 yx+ (2x +3z) ŷ +3yî. Calculate the curl and divergence…

A:

Q: Given f(x,y,z) = x2 + y2 + z2, find the maximum value of the directional derivative (df/ds) at the…

A: Consider the provided question,

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: Find the gradient of f(x,y,z) = (x² + y² +z²) ¯ - 1/2 Vf(-21.-2)=(1+Dj+k (Type integers or…

A: topic - gradient of a function

Q: Find the gradient of z = (7x + 4y)e. Assume the variables are restricted to the domain on which the…

A:

Q: Find the gradient of the function at the given point. w = 5x²y-7yz+z², (1, 1, -2) O 15i+ 26j+ 11k O…

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Q: Compute the gradient of the function f (x,y, z) = cos(x – y) + xe²z and evaluate this gradient at…

A:

Q: Let a be a real number and f(x, y) = 2ax²y + 8xy³. Let v = 3i – j and let Vf(x, y) denote the…

A: use the formula for gradient of a function.

Q: Find the gradient of f(x,y,z) = (x² + y² +z²) Vfl (2,-1,-2)=(₁+j+k (Type integers or simplified…

A:

Q: Find the gradient of the function f(x, Y, z) = y² ln(za), at the point (e, –1, 1) Vf(e, –1,1) =

A: The given function fx,y,z=y2ln(zx)

Q: Let a be a real number and f(x, y) = 4ax²y + 5xy³. Let v = 3i – j and let Vf(x, y) denote the…

A:

Q: Compute the gradient of the function at the given point. f(x, y) = 5x2 + 10y, (4,-3) Vf = 80i - 30j…

A: As per the instruction, we will answer the first one. Given: Now,         ∇f=fxi+fyj     =10xi+10j…

Q: Calculate the gradient of h(x, y, z) = x2 Z

A: Given h(x,y,z)=x1y3z. The objective is to find the gradient of h.

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

A: This question is simply based on formula of gradient

Q: 15. Compute the divergence of the gradient of a function f (x, y, z) = 3 x³ y² z3

A: The gradient of a scalar point function f(x,y,z) is given by the equation; Graf…

Q: Let a be a real number and f(z, y) = 3ax²y + 6zy³. Let v = 3i – j and let Vf(x, y) denote the…

A: Please see the answer in step 2

Q: Find the gradient of f at the indicated point f(x,y,z)=yz3-2x2; P(2,-3,1)

A: The formula to find the gradient is ∇f=∂fx,y,z∂x,∂fx,y,z∂y,∂fx,y,z∂z, that is partially…

Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vfl(-12,-2)=i+j+k (Type integers or simplified…

A: Given

Q: Let g(x,y,z)=2xe^y+yz^2. Use the gradient vector to find the equation of the tangent plane to the…

A: We will use definition

Q: determine all the functions f(x,yx,z) such that gradient f=2xi + zj + yk

A: Given that grad f=2xi+zj+yk find all functions

Q: Find the gradient of the function f(x,y,z)=y^2ln(xz), at the point (1,2,e) ∇f(1,2,e)=

A: Given f(x,y,z) = y2ln(xz)

Q: The gradient vector of the function f(x, y) = 2+ Ty at the point (1, 1) is %3D Select one: O True O…

A: The gradient vector of function f is given by: ∇f=∂f∂x,∂f∂y Here, ∂f∂x=12xyy=y2xy∂f∂x=12xyx=x2xy

Q: Find the gradient of the function at the given point. w = x tan(y + z), (12, 13, -11) Vw(12, 13,…

A: Gradient of w=xtany+z at 12, 13, -11

Q: For a scalar function f(x, y, z) = x? + 3y2 + 2z?, the gradient at the point P(1, 2, - 1) is

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Q: Find the gradient of the function z(x, y) at the given point P: z = cos(x² + y²), P(3, — 4).

A: The given function is z=cos(x2+y2), P(3,-4).

Q: Find the gradient of the function f(r, y, z) = z* In(yx), at the point (e, 1, -2) Vf(e, 1, -2) =

A:

Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vfl (1,2,2)=(i+₁+O (Type integers or simplified…

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Q: Calculate the gradient, Vƒ, for the following scalar functions (a) ƒ = xyz. (b) ƒ = x² + y² + z².…

A: