Question: Problem 4: 1) Let us consider the following scalar and vector fields: Evaluate: f(x, y, z)=x.cos(log(x*y +2)) + e-zx cos(x +2) F = |

Problem 4: 1) Let us consider the following scalar and vector fields: Evaluate: f(x, y, z)=x.cos(log(x*y +2))

Problem 4: 1) Let us consider the following scalar and vector fields: Evaluate: f(x, y, z)=x.cos(log(x*y +2)) + e-zx cos(x +2) F = | e-yx.Arctan(x) z + cos(xz) VxVf(x,y,z) and V.VXF y"+cy'+y=r(t) 2) Find the steady state solution of: With c> 0 and r(t) sin(31) 5 (The steady state solution is the solution of the nonhomogeneous equation). 3) Given a mass of density 1, in a region T of space, find the moment of inertia ab the x-axis if - (x +2)dxdydz T is the cone y + z x, 0xsh 4) Evaluate: F(r). dr where F(r)-(x) C is the boundary region of the triangle with vertices (0,0), (3,3) and (3,6).

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