Consider F and C below. F(x, y, z) = yzex² i + exZj + xyexz k, C: r(t) = (t² + 2)i + (t² − 2)j + (t² − 3t)k, 0≤t≤ 3 (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate J F. dr along the given curve C.

Q: Find f, (x.y) and f, (x,y). Then, find f, (1,-3) and f,(-1,- 2). f(x,y) = - 5xy + 2y +6

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Q: Find V. (F x G), if F(x, y, z) = 16xi +j+8yk and G(x, y, z) = xi + yj - zk.

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Q: 4x + y² R² → R²: f(x, y) = 2xy +1) If there exists a function F(x, y). such that VF(x, y) = f (x,…

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Q: Determine the expression for F(x, y, z) given the function F(x, y, z) = 2x²y = xz² + 3y²z.

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Q: evaluate the function at the given point. f(x,y)=x2+y2, D={(x,y):0<=x<=1, 0<=y<=1}

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A: we have to find the domain for f(x)

Q: For the function f(x,y,z) = In (8x + 7y+ 10z), find fy, fy, and f,. fx fy =D Iz =

A: given,      fx,y,z=log8x+7y+10z

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A: Solve this by maximizing the function in two variable Partially differentiating the function with…

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Q: Find f, and f, for f(x, y) = 10(9x – 8y+ 12)°. fx(Xx.y) = f,(x.y) D

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Q: Write the Linear Approximation to f(x, y) = x(1 + y)-¹ at (a, b) = (8, 1) in the form f(a+h,b+k)…

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Q: . Find div(F x G) = V · (F × G). F(x, y, z) = i + 9xj + 3yk G(x, y, z) = xi - yj + zk div(F x G) =

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Find all values of x and y such that f (x, y) = 0 and fy(x, y) = 0 simultaneously. f(x, y) = x² +…

A: The given function .The aim is to find all values of  and  such that .

Q: Find V x F for F(x, y, z)= - -xZ + y² i+ -yz x² + y² =j+√x² + y²k.

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Q: Evaluate f(х, у) ds. f(x, у) %3D у + 3 s: r(u, v) = ui + vj + 4vk, 0 sus 1, 0svs 4

A: Given: fx,y=y+3 S:ru,v=ui+vj+4vk, 0≤u≤1, 0≤v≤4 Differentiating r with respect to u, ru=1,0,0…

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Q: b) If it is possible, find the function f(x, y) = u(x, y) + iv(x, y). where u(x, y) = x2 + 2xy- y²…

A: That's easy. Have a great day!!!

Q: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

A: Given function:To find Known facts:

Q: Find all values of x and y such that f(x, y) = 0 and f(x, y) = 0 simultaneously. f(x, y) = x² + 4xy…

A: To find all values of  such that  simutaneously.

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Q: 04 Let f(x) be a contineous function such that Ler - 5/W)dx = = 4 and =9, then a) 81 b) 101

A: Use definite integration property

Q: (b) (c) Explain the differentiability of f on R by using definition. 1 Let f' be the first…

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A: As per our guidelines we are allowed to answer only one question. Kindly repost the other question…

Q: Evaluate the function g(x, y) at the point (4, –8). x2 + y2 g(4, –8) =

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