Verify the linear approximation at (2, 0). f(x, y) = y + cos²x ≈ 1 + Left f(x, y) = √y + cos2x. Then fx(x, y) = and fy(x, y) = differentiable at (2, 0) by this theorem. We have fx(2, 0) = f(x, y) = f(2π, 0) + fx(2, 0)(x-2π) + ƒу(2π, 0)(у - 0) = and fy(2, 0) = Both fx and fy are continuous functions for y > so the linear approximation of fat (2π, 0) is so fis