Real analysis:

For n 6 Zoo, let fa(x) be the function on the interval [0, 1] defined as follows: fn(z) = 2n - n-r IA JA IA 0 2. we have fo fr(x)dx = 1. 2. Show that the pointwise limit of the sequence f,(r) is the zero function, and conclude that lim 1+00 fn(x)dx # lim fr(x) ) dx. 7+00 (Here, limn-+ fn(ar) indicates the pointwise limit which you just computed.)For n a postlive integer, let g, (x) be defined for r e R as follows: In(x)= 4. Show that 100 lim lim gn() ) dr. -DO In-+00 (Here, lim, . gn (@) indicates the limit which you just computed.)