Consider the heat equation for u(t, x) on the unit interval, du = 0, 0 < x < 1, t > 0. Solve the initial-boundary (a) value problem where the initial conditions are u(0, x) = 0, %3D and the boundary conditions are mixed and inhomogeneous, du (t,0) = 0, u(t, 1) = sin(wt). %3D || (b) the limit that the frequency of the boundary condition w → o. Explicitly compute u(t, 0) in

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