Prove that ∆ + ∇ =∆/∇ −∇/∆

Q: What is the gradient vector of a differentiable function ƒ(x, y)? How is it related to the…

A: The objective is to write what is the gradient vector of a differentiable function ƒ(x, y) and how…

Q: exist. :) Compute the linearization of f(x, y) at the point (x, y) = (1,1). %3D

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Q: Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to (-1, 0,…

A: By Fundamental theorem line integral,we have Where C is curve joining to

Q: Verify if div(curl F) = o for = (x - y) i+ (x +y)j+zk.

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Q: calculate div(F) and curl(F).  F = (x, y, z}

A: Answer(a): div(F)=3

Q: Find the force on one side of a plate bounded by x = y² and x = 2 - y² which is submerged vertically…

A: Given the plate is bounded by x = y2 and x = 2 - y2 and the plate is vertically submerged such that…

Q: .    Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to…

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Q: Verify Stoke's theorem for the vector point function yz2 (xz² .3 + ex over the surface S of the cube…

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Q: .    Find work done by the gradient of f(x, y, z) = zexy+ 2y2z  along the path from (1, 2, 4) to…

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Q: 4. Show that the covariant derivative of the metric tensor vanishes: V,gjk = V,9k = 0. %3D

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Q: What is special about the derivatives of vector functions of con-stant length? Give an example.

A: What is special about the derivatives of vector functions of constant length

Q: 2. Suppose that f (1,2) = 3 and that the directional derivative of ƒat point (1,2) in the direction…

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Q: Explain why the family of vector-valued functions that are the antiderivatives of a vector-valued…

A: The family of vector-valued functions that are antiderivatives of a vector-valued function will…

Q: Each of the two functions v and u with the variables x and y satisfy he Cauchy - Riemann equations,…

A: Let,  u=x2-y2, v=2xy

Q: How is the linearization of f(x, y) centered at (a, b) defined?

A: To define linearization of a function f(x,y) at point (a,b).

Q: 2. Find the gradient vector at the indicated point f(x, у, 2) 3 ху — In (2),. (2, -2,2)

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Q: Let F(x, y, z) =2x2+3y2+4z2. For which unit vector 0 will the directional derivative DoF at…

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Q: Determine if u and v u = (cos 0, sin 0,–1); v= (sin 0.-cos 0,0) are orthogonal

A: We have to determine if u and v are orthogonal   The given vectors are u=cosθ, sinθ, -1v=sinθ,…

Q: he upward flux of

A: Introduction: Let F be a function and let the region is S, then the flux of the function is given…

Q: Prove that the vector given by (sin ysinh x + cos ycosh x) i + (cos y cosh x- sin ysinh x) j is a…

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Q: Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional…

A: Given that ∇ƒ(9, 9) = ⟨3, 1⟩. Note that w = (1, -1) is not a unit vector. Its unit vector along same…

Q: The gradient vector for the surface xy + xz + yz = 1 at the point (1, 1,0) is (1, 1,0). Select one:…

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Q: Find the direction in which the maximum rate of change occurs for the function f(z,9)2zsin(ay) at…

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Q: Find work done by the gradient of f(x, y, z) = zexy+ 2y2z  along the path from (1, 2, 4) to (-1, 0,…

A: The gradient of f(x, y, z) is:

Q: The gradient of f(x, y) = xy at (x, y) = ( – 3, – 2) is %3D

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Q: Calculate the directional derivative of f(x,y)= In( Vx +y ) at point (1,1) in the %3D direction of v…

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Q: Calculate div(F) and curl(F).  F =〈x^2, y^2, z^2〉

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Q: Find First and second derivatives of Funchion . tm - (e-a -a)(e-a+a) Where a is parameber

A: To find a first and second derivative by first simplify the equation and finding it's value at x=0

Q: Determine the type of points on the x(u, v) = (u, v, u²) surface. Differential geometry

A: Given point is Xu,v=u,v,u2.  This point is of the form Xu,v=fu,v,gu Let Xu,v=xi+yj+zk. Then,  x=u…

Q: what local linearizatoin of the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1)  (show all steps…

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Q: let 2 Vector tield A=x B=y2 Find explicit expresom of Lie derivative L, CB)

A: Please find the answer in next step.

Q: 5. Compute the directional derivative and gradient of f(x,y,z) = 4x – y²e3xz at (2. –1.0) in the…

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Q: Show that whether if the co-vector w can be written as dø differential? w = y. (x +). dx + x. (+).dy…

A: Given:  w=y·x+y2· dx+x·x2+y·dy....(1)

Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional gives the rate of change of a function at a specific point in…

Q: The directional derivative of f(x, y) = xe + cosxy at P,(2,0) in the direction of the vector 3i - 4j…

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Q: Differentiate the function. y = In(In x) y' = %3D

A: Given y=ln(ln x)             y=ln(ln x).y'=ddx(ln (ln x))y'=1ln(x) . ddx(ln x)y'=1ln(x) . 1xy'=1x .…

Q: Find the directional derivative of the function f(z, y) = In(z° + y*) at the point (3, – 1) in the…

A: We can solve this as follows:

Q: 2. Calculate the instantaneous rate of change of g at the point (4, 1,0) in the direction of the…

A: Please see the attachment

Q: What is special about the derivatives of vector functions of constant length? Give an example.

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Q: Find the directional derivative of the function f(x, y) = In(x +y°) at the point (2, 3) in the…

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Q: 4. Show that the covariant derivative of the metric tensor vanishes: V,gjk = V,gk = 0.

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Q: a. Find the direction in which the directional derivative of f(x,y), at the point (z, y) = (0,4),…

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Q: integral that line x = 0

A: As per the bartleby guidelines for more than three parts only three has to be solved. Please upload…

Q: Compute the gradient of f (x, y) = (x + 2) + xysin(y) at (0, 1)

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Q: Prove that the directional derivative of flay.2) = aysinz. direction v=i +2j+2k 1Is Sin Z at…

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Q: The gradient vector of g(x, y) = at (√√2,-1) is Vg(√2, -1) is equal to Select one: O True O False -

A: Given: The gradient vector of g(x,y)=x22-y22 at (2,1) is ∇g(2,1) is equal to <2,1>

Q: Calculate the directional derivatives of the function f(x,y) = x² – y? in the direction of the…

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Q: Determine where the resultant force acts measured from point O.

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Q: find inverse laplace of frs)= los-3 25-S %3D

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Q: Compute the directional derivative and gradient of at (2,-1,0) in the direction of the unit vector…

A: Dot product of A.B is ad+be+cf where A=<a,b,c> and B=<d,e,f>.