1, Let {mu}?c be a converging sequence with lirnit x. That isI limn mm\") = x. Show that \"nu-1 lim [emu] 2 ca: for all c E R 2, If S and T are any two sets, the Cartesian product S x T of S and T is defined as the set of all ordered pairs (s,t) with .9 e 5' and t e T. SxT={[s,t):sES,tET} Now suppose S and T are both intervals of the real line, so both are convex. Show that S x T is a convex subset of R3. (Hint: a sketch could be helpful)