1. The accompanying figure shows two polygonal paths in space joining the origin to the point (1, 1, 1). Integrate f(x, y, z) = 2x – 3y? – 2z + 3 over each path. (0, 0, 0) •(1, 1, 1) (0, 0, 0) (1, 1, 1) ' (1, 1, 0) (1, 1, 0) х Path 1 Path 2

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A: Given,uxx=utt-sin x , x∈0,1, t>0Boundary conditions: u(0,t)=ux(1,t)=0 , t>0…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x+ 8y + 12z on the elipse…

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Q: 39. Find all points on the portion of the plane x+y+z= 5 in the first octant at which f(x, y, z) =…

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A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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A: Answer is mentioned below

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A: We will convert the dynamic system from Cartesian (x,y) plane to Ploar (r,θ) plane.

Q: (2) Find the integral (0,2,0) and (0,0,1). where D is the tetrahedron with vertices (0,0,0),…

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Q: 2. Find the value of xy dx + Vy2 + 1dy, where C is the path shown on the graph below. (Hint: Use…

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A: Solution is below

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Q: 5. Find the solution u(x, t) of uz = conditions u(0, t) = uz(1, t) = 0 and the initial condition…

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Q: (2) Solve the Laplace equation with the following boundary condi- tions. Uzr + Uyy = 0, 0 < « < a,0…

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Q: (b) || 6xy dV, where E lies under the plane z 1+x + y and above the region in the xy-plane bounded…

A: A triple integral involves the integral with respect to x,y, and z. In this problem, we have to…

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Q: 15. Evaluate the line integral J. (3xy* - 6xy ]dx + (4x'y - 3x) dy, where C is any path from (1, 2)…

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Q: y" +3y + 2y = denkleminin özel çözümü y; aşağıdakilerden hangisidir? %3D +1 O a. y5 = ze2 - e In(1+…

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Q: Let us consider the hyperbolic PDE is utt with the initial conditions c2U, 0 0 %3D u(x, 0) = P1(x)…

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Q: Evaluate the triple integral.  (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2)…

A: The given triple integral is,

Q: 3.4.6 Use Green's theorem in a plane to evaluate of 10x9²³- [(xy²-y) dx + (x + y²) dy] C as a double…

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Q: Find the Wronskian of a given set {yı, y2} of solutions of 6. y"3(x21)y- 2y 0, given that W(T) = 0.

A: Given the differential equation and the value of the wronskian at pi as:

Q: (6) Evaluate the line integral / r²ydx + xy°dy, where C is the square with vertices (0,0), (1,0),…

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Q: Example 6: Evaluate ez dz dy dx E Where E is enclosed by the paraboloid Z = 3+ x? + y² , the…

A: The given problem is to evaluate the given triple integral of given function ez for which region E…

Q: Evaluate the path integral between the points A = (1,3) and B = (2,5) of: B *(x²y + 2y)dy, with y =…

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Q: Obtain the Solution x, y > 0, xy > 1 of the PDE 2y on the x+y 1 Uxy such that u = x+y 0, ux…

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Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

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Q: a) Find the solution for u(x, y, z) yux − xuy + uz = u2 u(x, y, 0) = 1/y

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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A: Here we have to evaluate the integral ∫cx2dx+xe-ydy where C is the closed path along the triangle in…