Consider F and C below. F(x, y, z) = yzexZi + eײj + xyeײk, C: r(t) = (t² + 2)i + (t² − 1)j + (t² − 4t)k, 0≤t≤ 4 (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate ICF F. dr along the given curve C.

Q: f= (2xy+ 3x²)ē+ (x² – 2yz + 2y)ē, – (e² + y²)ēz

A: Given

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A: The given function .The objective is to find the regions that are the domain of the function.

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A:

Q: For the function, evaluate the following. f(x, y) = x2 – y – xy + 2 (a) f(0, 0) (b) f(1, 0) (с) f(0,…

A:

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

Q: For the function f(x,y) = 7x² + 6y², find f(x + h,y)-f(x,y) = h f(x+h,y)-f(x,y) h

A:

Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: Find the largest domain (in R²) for the function 1+ Vr+ Vỹ x² + y² f(x, y) : =

A: Given: The function f(x, y)=1+x+yx2+y2.

Q: Let f(x, y) = x²y. Compute and simplify each of the following: (a) f(x + h, y) – f(x, y), and (b)…

A:

Q: Let xj = xo + hj for j = 0, 1, 2. Use the quadratic polynomial interpolating f at those nodes to…

A:

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A: Consider the given function : f(x,y)=(1+x+y)e-xy

Q: Given f(x, y) 90x + 80y - 2 – 4y? – xy, and evaluate f(8, 5). f(8, 5) = %3D

A: Given : fx , y = 90x + 80y - 2x2 - 4y2 - xy  To fine : f8 , 5 Solution : For value of fx , y , put x…

Q: he function f(x)=3x2+2x

A: Introduction: A function is bijective if it is both injective and surjective and a function f(x) is…

Q: Find f f(x,y) dA, where f(x, y) = x and R = [5, 10] × [-5, –4]. SSR f(x, y) dA=

A: The given function is f(x,y)=x, and the domain is x,y∈5,10×-5,-4. To Evaluate: ∬Rf(x,y)dA.

Q: Find fx and fy for f(x,y) = y In (x + 8y). || fy = y x+8y

A: Step 1: Step 2: Step 3: Step 4:

Q: Consider the function f(x, y) = x² – 6x + y? –- 2y + 10. Sketch the domain of the function h defined…

A:

Q: Write f(z) = Im(z - f(z) = u(x, y) + iv(x, y). 3z) zRe(z²) - 5z in the form ○ a. (4y+x³ − xy²) +…

A: Step 1Step 2Step 3 : Step 4