Show that potential function U= x2+y2+2z2 satisfies Laplace equation
∇2U=∂2U∂x2+∂2U∂y2+∂2U∂z2=0,\nabla^2U=\frac{\partial^2U}{\partial x^2}+\frac{\partial^2U}{\partial y^2}+\frac{\partial^2U}{\partial z^2}=0,∇2U=∂x2∂2U+∂y2∂2U+∂z2∂2U=0,
∂U∂x=2x,\frac{\partial U}{\partial x}=2x,∂x∂U=2x, ∂U∂y=2y,\frac{\partial U}{\partial y}=2y,∂y∂U=2y, ∂U∂z=4z,\frac{\partial U}{\partial z}=4z,∂z∂U=4z,
∂2U∂x2=2,\frac{\partial^2U}{\partial x^2}=2,∂x2∂2U=2, ∂2U∂y2=2,\frac{\partial^2U}{\partial y^2}=2,∂y2∂2U=2, ∂2U∂z2=4,\frac{\partial^2U}{\partial z^2}=4,∂z2∂2U=4,
∇2U=2+2+4=8≠0,\nabla^2U=2+2+4=8 \not =0,∇2U=2+2+4=8=0,
function U does not satisfy Laplace equation.
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