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

 

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Problem 4: 1) Let us consider the following scalar and vector fields: Evaluate: f(x, y, z)=x.cos(log(x*y² +2²)) + e-zx² cos(x³ +2³) F = | e-yx.Arctan(x) z³ + 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 - (x² +2²)dxdydz T is the cone y² + z² ≤ x², 0≤xsh 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). Problem 4: 1) Let us consider the following scalar and vector fields: Evaluate: f(x, y, z)=x.cos(log(x*y² +2²)) + e-zx² cos(x³ +2³) F = | e-yx.Arctan(x) z³ + 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 - (x² +2²)dxdydz T is the cone y² + z² ≤ x², 0≤xsh 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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The provided image shows a problem set with three distinct problems Specifically it requires evaluating vector calculus expressions finding the steady state solution of a differential equation and com... View the full answer