Verify the linear approximation at (0, 0). f(x, y) = root y + cos^2x approximately 1 + 1/2y Left f(x, y) = root y + cos^2x. Then fx(x, y) =and fy(x, y) = . Both fx and fy are continuous functions for y > , so f is Differentiable at (0, 0) by this theorem. We have fx(0, 0) = and fy(0, 0) = , so the linear approximation of f at (0, 0) is f(x, y) approximately f(0, 0) +fx(0, 0)(x - 0) + fy(0, 0)(y - 0)= .