Please help with practice example problems 3 and 4.

3) Let D = {(a:,y) E R2 I 0

3) Let D y) G R2 | 0 < + Y2 4}. Give all boundary points of D. Is D open, closed or bounded? Justify all your answers. The related definitions of closed and bounded set are as follows: Closed: A set D is closed if it contains all of its boundary points. Bounded: A subset D of R n is bounded if it is contained in some open ball Dr (O). For example the interval [ 1, 5) is neither open nor closed since it contains some but not all of its endpoints. It is bounded since it is contained in the open interval (O) 4) Assume you are given the surface S with equation T + + E 1 4 (a) Find the equation of the tangent plane to S at the point (T, V'6, 1). (b) Find a point on the surface S so that the tangent plane to S at that point contains the point (3, O, O). (c) Give an equation for and geometrically describe the set of points on S so that the tangent plane to S at those points contains the point (3, 0, 0).