a. Find a function (f(x,y,z)) such that (F = Vf(x,y,z))? b. Use part (a) to evaluate (F. dr ) along the given curve (C)? F(x,y,z) (6xyz) î + 3x²zj + (3x²y + 5z) k C is the line segment from (1, − 1, − 2) to (− 1,2,4) - =

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Q: The function g(x, y) has tangent lines at the point (1, 2) with directions and . Find Vg (1,2).…

A: Given that:  Tangents at point (1, 2) are:  <2, 0, 8> and <0, -1/3, 2>

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A: given,      fx,y,z=log8x+7y+10z

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Q: Calculate the distance between the following lines.

A: Arrange the given lines in standard Cartesian form.

Q: 2. Construct the cubic spline that intersects with function f(x) at these points (1,-5), (0,3),…

A: Given Data: To construct the cubic spline that intersects with function  at the points , ,  and use…

Q: . Sketch the level curves of the function f(x, y) = x² + 2x + y² – 6y corresponding to the z-values…

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Q: Find the distance from the point (4, 9) to the line y = 2x.

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Q: Determine the indicated values for the function f(x,y)=2x²y. O8y8 O2y1 O1y4 O 10 y 8 fx(2.1); f,…

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