Consider F and C below. F(x, y, z) = yzexi + ex² + xyek, C: r(t) = (t² + 5)i + (t² − 1)j + (t² − 2t) k, Osts 2 (a) Find a function f such that F = Vf. f(x, y, z) = /F. (b) Use part (a) to evaluate F. dr along the given curve C.

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Q: The function f(x, y) = x² + y² √x² + y² +1-1' (a) {(x, y) = (0,0)} (b) {(x,y) = R²2} 2 if : (x, y) =…

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Q: 5. Express the given function using unit step function: * [t f (t) = 0st<4 2 , t24 O A.) f (t) = t…

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Q: Locate and classify the local extremum of the function f (x, y) x² + y? – 8x – 2y + 6. | -

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Q: Let f(x, y) = 6x³ – 3e²y + 9y. 8u? – 2v || Assume that y = 2uv. Consider the composite function 9(u,…

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Q: Show that ƒ(z) = 3x² + 2x − 3y² − 1 +i (6xy + 2y) is differentiable at every point in the plan -

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Q: Let F(x, y, z) = (14xyz + 7sin(x))i + 7x²zj + 7x²yk. Find a function f such that F = Vf. f(x, y, z)…

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Q: Given a function f(x,y,z) = 5x² In (7y + 3z). Find the domain of the function. %3D o {(xy,z) |z >…

A: Use logarithms definition to choose the correct answer.

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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: Consider F and C below. F(x, y, z) = yzexZi + e²j + xye*²k, C: r(t) = (2 + 4)i + (t² – 1)j + (t² -…

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Q: Advanced Math Question

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

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