Consider F and C below. F(x, y, z) = yzi + xz j + (xy + 14z) k C is the line segment from (2, 0, -2) to (4, 5, 1) (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate Ic F. dr along the given curve C.

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A: (a) Since the contour line which passes through point 2, 1 has a corresponding value 3. Therefore,…

Q: Let F = (y – x, ry) and let C be the line segment from (2, –3) to (1, –1). %3D Evaluate F. dr.

A: We wil first equation of parametric equation of line segment

Q: 2. For F(x, y, z) = (6xsin y+10x=' )i + (3x² cos y-4ye* −2y²z³)j + (-2y³e² +15x²2²)k, find a…

A: Given Data: Let us consider the given data, Fx,y,z=6x sin y +10xz3i+3x2 cos y -4yeyz-2y2zeyzj…

Q: a. Find a function (f(x,y,z)) such that (F = Vf(x,y,z))? b. Use part (a) to evaluate (F. dr ) along…

A: We have to evaluate the ∫CF.→dr→.

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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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Q: 5. nts) Let F =, use Green's Theorem to evaluate F. dr where the curve C is C the curve shown in the…

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Q: Please review the screenshot and provide a solution. Please make sure that the solution is formatted…

A: Approach: Understand the problem statement:The goal is to evaluate the integral ∫f(x,y,z)ds over a…

Q: • Let S be the graph of f(r, y) = r² + y² – 2r + y for (r, y) E D = {(r, y) :2² + y² < 4 and z + y 2…

A: The function is fx, y=x2+y2-2x+y The region D is x, y: x2+y2≤4 and x+y≥0 The edges are x2+y2=4 and…

Q: Consider F and C below. F(x, y, z) = yz i+xz j + (xy + 10z) k C is the line segment from (2, 0, -1)…

A: I have explained everything with in the solution. Please go through that.

Q: Let C be the curve.

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Q: E.g. Let f(x, y) = x² - 2xy + y². The graph and contour diagram of f is given below right. Compute…

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Q: Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 12z) k C is the line segment from (3, 0,…

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Q: Let F = (3y + 2) i + (4x – 22) 7 + (3x – y) k Find Sc FdF where C is a line segment 8. %3D from A(2,…

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