Let f_(n):[0,2]->R be a sequence of functions defined by
f_(n)(x)={(0,x<(1)/(n+1),),(sin^(2)((pi )/(x)),(1)/(n+1)<=x<=(1)/(n),),(0,x>(1)/(n).):}
Show that {f_(n)} converges to a continuous function but not uniformly.
2.Let fn:[0.2]->R be a sequence of functions defined by
n+1
0.
x>1.
Show that {fn} converges to a continuous function but not uniformly
