Final answer:
The student is asked to compute the linear approximation of the function f(x,y) = x(1 - y)⁻¹. Without a specific point to approximate around, the general formula for the linear approximation in terms of the function and its partial derivatives is provided.
Step-by-step explanation:
The question is about finding the linear approximation to the function f(x,y) = x(1 - y)⁻¹. A linear approximation is applied to a function at a point to approximate the function's value near that point using the tangent plane at that point. Assuming we are approximating around the point (x0, y0), where both x0 and y0 are close to zero, the linear approximation can be expressed as f(x,y) ≈ f(x0, y0) + fx(x0, y0)(x - x0) + fy(x0, y0)(y - y0).
To compute this approximation, we would need to calculate the partial derivatives fx and fy at the point (x0, y0). However, the question does not specify the point around which to approximate, nor is there enough information provided to complete the approximation.