(4) Consider the surface given by 4x2 + 9g2 - 22 =0. (This is an elliptic cone.). This is the level surface F(x, y, z) = 0 where F(x, y, z) = 4x2 + 942 - 22. (a) Verify that P(2, 1, 5) is on the surface. (b) Compute the gradient of F(x, y, z) at the point P(2, 1,5). This 3-D gradient vector will be pointing from P(2, 1, 5) in a direction that is orthogonal to the surface. (c) Find an equation for the tangent plane of the surface at P(2, 1, 5). Hint: the gradient VF(2, 1, 5) is a normal vector to the tangent plane.(d) The upper half of this elliptic cone is the graph z = f(x, y). What is the function f(x, y)? (e) Find the equation for the tangent plane to the graph at the point (2, 1, f(2, 1)) by using the formula z = f(a, b) + fx(a, b)(x - a) + fy(a, b)(y - b). (f) Verify that the equations found in parts (c) and (e) are equations of the same plane.(g) The tangent plane from part (e) is the linear approximation. (Linear approximation is just another name for the tangent plane.) Use the linear approximation L(x, y) = f(a, b) + fx(a, b)(x - a) + fy(a, b)(y -b) to approximate f(1.9, 1.1). Do this by computing L(1.9, 1.1). Compare your answer with f(1.9, 1.1)