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The function f(x, y) satisfies the Laplace equation ∇²f(x, y) = 0 on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3. The numerical value of f(0, 0) is:

1. 0
2. 2
3. 3
4. 1

Correct answer: 3

Solution

The function f(x, y) satisfies the Laplace equation, which implies that it is harmonic. For harmonic functions, the value at the center of a circular domain is equal to the average value on the boundary. Since the boundary value is constant at 3, the average, and thus the value at the center f(0, 0), must also be 3.

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