Let f = f(x,y, z) be a sufficiently smooth scalar function and F = Vƒ be the gradient acting on f. Which of the following expressions are meaningful? Of those that are, which are necessarily zero? Show your detailed justifications. (a) V· (Vf) (b) V(V × f) (c) ▼ × (V · F) (d) V · (V × F)

Q: Calculate the gradient. f (x, y) = cos(x^2 + y)

A: Calculate the gradient. f (x, y) = cos(x^2 + y).

Q: Let g(u) be a differentiable function, and let f(x, y) = g(x² + y²). (a) Show that yfx = xfy. (b)…

A: let g(u) be a differentiable function, and let f(x,y)=gx2+y2. Then we have to answer the following..

Q: Find the gradient of the given functions in Exercises 37–39. 37. z = x2 sin y + y sin x 38. z =…

A: As per company guidelines, I can solve only one question.

Q: Determine the gradient of the given function. a. f(x,v.z)=sin( -)+zży²x b. f(xV2)= 4xy? c. flx,v.z)…

A: a) The gradient of a function is given by ∇fx,y,z=∂f∂xi+∂f∂yj+∂f∂zk Given function is…

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 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: A. Find the gradient of the function. f(x,y. z) = 3x y + cos(32)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the gradient of f(x, y) = y ln x + xy2 at the point (1, 2).

A:

Q: What is the gradient of f(x, y) = x² - y4 at the point (5,2)? O 5i + 16j O -15i-16j O -6i + 13j O…

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Q: 2. Find the gradient of the function f(r.y) In(r y²) at the point( 1, 1).

A:

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: Let F(x,y,z)=(3x2y) i+(x3+y3)j Find a function f such that F=gradient of f

A: Find the function f

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

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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: Let f(x,y)= In(x'+y): a) Calculate the gradient of fat (2, 1) b) Let x(f)=t+1 and y(r)=r. Find…

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Q: Find the gradient of the function: f(x, y, z) = x'y + = OF = (7x + 6x°)i + 3y²j + k %3D OF = 7x°y°i…

A:

Q: Find the gradient of the function f(x, y, z) = √(x2 + y2 + z2), and the maximum value of the…

A: The given function is fx,y,z=x2+y2+z2

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

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Q: Let f(x, y) = x² + In(2x – y). Find the gradient Vf(x, y) at the point (1, 1). O O O O

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Q: 1. Consider the function f(x, y, z) = (x+ 2y)2 + 3.x2 + 22. Compute: (i) The gradient of f and the…

A: Note:- As per our guidelines, we can answer the first three sub-parts of this problem. Please…

Q: The gradient of f(x, y) xy at (x, y) = (– 1, 1) is

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

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Q: Use the gradient to find the directional derivative of the function at P in the direction of Q h(x,…

A: Use the gradient to find the directional derivative of the function at P in the direction of Q h(x,…

Q: Let F(x, y) = [2ry² +x, 2r²y + y]. Find all functions f with gradient F. Find the derivative of f in…

A: # we are entitled to solve 3 subparts at a time ,please resubmit the other subparts if you wish to…

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: 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: 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: Find the gradient of the function w = x tan( y + z), at the given point (4, 3, −1)

A:

Q: Assume that f (1,2) = 4 and f (x, y) is differentiable at (1,2) with fx (1,2) = 2 and fy (1,2) = 3.…

A: Formula Used:-Linear approximation of f(x, y) is f(x, y)=f(a, b)+fx(a, b)(x-a)+fy(x-b)

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)=xy+yz+xz at point P(1,2,3).

A: As we know that the expression for the gradient is: ∇fx,y,z=i∂∂x+j∂∂y+k∂∂zfx,y,z 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: Find the gradient of the function f(x, y) = sin(x + 2y) O cos(x + 2y) [2î+î] cos(x + 2y) [i+1] O…

A:

Q: Find the gradient of the function f(x,y, z) = xy°z³ at the point (1,1,1).

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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: Calculate the gradient of f(x, y) = cos(x³ + y). %3D A) V ƒ = –3x² sin(2³ + y) – sin(æ³ + y) B) Vƒ =…

A:

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: 1. Consider the function f (x, y, z) = 2°y – xyzešzy Compute the gradient of f.

A: Let's find.

Q: B. Find the gradient of the function at the given point. 1 f(x, y, z) = (x² + y² + z²)¯2 + In (x y…

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Q: Let f(r,y, z) = x² + 3x°y + z°, g(u, v) = (u² + v², uv, 3u – 2v). Find the derivative of f(g(u, v))…

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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 In(x² − y) – 1, X Vz(2, 3) = Z at the given point. (2, 3)

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Q: What is the gradient of f(x, y) = x² - y4 at the point (5, 2)? O 5i + 16j O -15i-16j O -6i + 13j O…

A:

Q: Suppose directional derivatives of the scalar function f(P), at a point P = (x, y), in the…

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Q: Calculate the gradient of the function f(x, y) = cos (4z² – 4y) O a.-8z sin (4x2 4y)i + 4 sin (4x2 –…

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Q: (3) Find the gradient of f. (a) f(z,y) = r²y³ (b) f(x, y) = sin(x – y) (c) f(x,y) = In(x² – y²)

A: Given:  (a) fx,y=x2y3 (b) fx,y=sinx-y (c) fx,y=lnx2-y2 To determine: The gradient of f. Concept…

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

A: