Let f(x,y) =sin(xy-x-3y+3) a) Find the domain and range of f b) Factor the argument on the sin function. Does this factored form give any hints about the appearance of the surface z = f(x,y) c) Find a relationship for the x cross-sections by letting x = k, k & R. Then, tabulate the relationships for k = 0, 1, ..., 6 and sketch the relationships for k = 3, 4, 5, 6 on the interval y € [1-π, 1+π] and with respect to the cross-sections for k = 4, 5, 6, describe the cross-sections for k = 0, 1, 2 d) Find a relationship for the level curves/contours by letting z = m, m & R. By recognising the periodic nature of f and ensure that the relationship accounts for

Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.

Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.