Ready solution of the problem. The sorcerer of Arutyunov. Task number 243.

241 - 250. Given a function z = f (x, y) and two points A (x0, y0) and B (x1, y1). It is required: 1) to calculate the value z1 of the function at point B; 2) calculate the approximate value z1 of the function at the point B based on the value z0 of the function at point A, replacing the increment of the function with the transition from point A to point B by the differential, and estimate the percentage error arising when the increment of the function is replaced by its differential; 3) form the equation of the tangent plane to the surface z = f (x, y) at the point C (x0, y0, z0)

243. z = x2 + 3xy-6y; A (4; 1), B (3.96, 1.03)

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Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)