I use a theorem : let from left as k->infinite , and f be continuous if , as
clearly , is a continuous on and let converges to 1 from left.
And this is infinite as k->infinite
Oh yes! I have heard a theorem like that before. So I follow you up until the point where you let . It is an increasing function, but is there a way to find such {x_k}? EDIT: or is it arbitrary?