Please show all work, step by step. written and explained as neatly as possible. Thank you so much!!

We 11 it) Find the poihtwise limit for x E R. b) IS the limit uniform on R? C) IS the limit uniform 0n [0, 1]? (9 ) By the given question lim DC e lim e kim 1 -7 00 e e (0 ) C I XO Ans Now Let E.= I for any KER Then Taking Natural logarithm both side n Jolme = 1 x z n log (n ) for any ZEN FXER It is clear from the definition of uniform Continuity , continuity fails for E.= I Thus, limit Is not uniform in R . Ans( C ) Now , Let E 20 g(x ) = 2" increasing function for any X E CO , I] and any new So 1 = ez em , em ce So we Can conclude 1 - 2 .e e