Problem #8: Use Divergence theorem to find the outward flux of F = (4x², e, cos³(y² + x)) of the cube in R³ bounded by the planes x = 0, x = 2, y = 0, y = 2, z = 0, z = 2. Problem #8: Just Save Submit Problem #8 for Grading Problem #8 Attempt #1 Attempt #2 Your Answer: Your Mark: Attempt #3

Q: 2. Write the formula for tangent plane of a function f(x,y) at a point x = a.y=b. How does this…

A: Conisder a function f(x,y).We need to find the tangent plane at x=a,y=b.Let z=f(x,y) and…

Q: 2. a). Find the velocity and acceleration of a particle whose position function is x(t)=…

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Q: 4. Let f(x, y) = 2TY x = In 2 g and y = In s. . a. Find the equation of the tangent plane to f(x, y)…

A: Let f(x,y)= 2xy , x=t/ln2 and y= lns Here we have to find the equation of the tangent plane to…

Q: c) Given the scalar function p(x, y, z) = x²e - y³ + cos 2z. Find the directional derivative of p(x,…

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Q: 2. Suppose the elevation of a hilly contryside is given by the function E(z,y) = sin z + cos y. %3D…

A: The solution of given problem is followed by

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A: In algebraic topology, two topological spaces are said to be homotopy equivalent if there exists a…

Q: 11. Let F(x, y, z) = = (), and let P represent the path that follows the from (1, 0, 1) to (0, 1,0),…

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Q: Let f(x, y) = 2 sin(x². y) + by³ where b is a real number. Suppose that the direction of maximum…

A: Here, we have used the concept that the direction of maximum change of function at a point is given…

Q: 2. § F•dï , where F = (ycos(x) – xy sin(x), xy + xcos(x)) and C is the C triangle from (0,0) to…

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Q: Find the equation for the tangent plane to the surface x- 5xyz+ y = - 7z at the point (- 1, -1, -…

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Q: 3. Given F(x,y)=(y,2x), find F-T ds where curve C is the parabola y=x from point (0,0) to point…

A: We use line integration to evaluate this.

Q: f (x, y) is a differentiable function with Vf(4,3) = 7i+ 5j. 2. Suppose w = (a) Find the directional…

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Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: = Problem #4: Find the equation of the plane that is tangent to the surface f(x, y): much as…

A: The equation of tangent plane to the surface  at point  isWe have given:

Q: 3. Given the vector equation r(t) = (3+4 sint, -2 + 4 cos t), 0 < t < 2n, you should recognize that…

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Q: 1. Find all points on the graph of h(x, y) = plane is horizontal. 3x²9x + 4 + 2y³ - 12y where the…

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Q: 4. Find the equation of the tangent plane at the point (-2, 1, -3) to the ellipsoid 22 + y? + = 3 4

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Q: 3. Use integration to determine the formula for the "equatior: given that : F(t) = ( 2t , 12e" , sin…

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