1. To identify the surface S, we need to analyze the given equation. However, it seems that the equation is missing, as only "z" is mentioned. Please provide the complete equation for a more accurate identification.
2. Once the equation for surface S is provided, we can find the tangent plane at the point (1, 0, 3). To find the tangent plane, we need the gradient of the surface equation.
The gradient of the surface equation gives the direction of the normal vector to the surface at any point. The equation of the tangent plane can then be written as:
(x - x1)(∂f/∂x) + (y - y1)(∂f/∂y) + (z - z1)(∂f/∂z) = 0,
where (x1, y1, z1) is the given point and (∂f/∂x), (∂f/∂y), and (∂f/∂z) are the partial derivatives of the surface equation with respect to x, y, and z, respectively.
To find the tangent plane at (1, 0, 3), we need the equation of the surface S. Please provide the equation so that we can proceed with the calculation.
Please let me know if you have any further questions or if there's anything else I can assist you with.