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15_2_21 - = r sin(2 r Both of these equations are satisfied...

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21. If F = r sin ( 2 θ) ˆ r + r cos ( 2 θ) ˆ = φ( r , θ) , then we must have ∂φ r = r sin ( 2 θ), 1 r ∂φ ∂θ = r cos ( 2 θ). Both of these equations are satisfied by
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