In part (a) of my questions I'm asked to show

I have done this, and part (b) asks me to consider a sequence of functions

,

then for each fixed determine the point at which the function attains its maximum value and hence, calculate

I'm told I may use part a. I'm not sure if is meant to represent x values in which case the max would be achieved (as I can see) at x = 1, but I can't see the relation with part (a) by doing that.