Consider the following sequences of functions on their respective domains. For each
of the following check if there is any point wise limit and if yes, then identify it.
Further check if the point wise convergence is uniform as well (on their respective domains). Need to give justifications.
Comment whether the respective sequences are uniformly bounded or not.
Comment about continuity and differentiability of the limiting functions their re- spective domains.
(i)fn(x)= nx/(1+nx) on[ 0,1]
(ii) fn(x) = xn on [0, ¾]
(iii) f (x)= 1/(1+ xn)on[0,1].