A function is defined as fx=limn→∞  cos2nx,         if  x<01+xnn,       if  0≤x≤111+xn,        if x>1which of the following does not hold good?

f0-=limn→∞  limn→0-  cos2xn               = a  value  lesser  than  1∞=0f0+= limn→∞  limn→0+  1+xn1n=1Also, f(0) = 1. So, the function is discontinuous at x = 0.Further,  f1-=1;  f1+=0;  f1=1.So, the function is discontinuous at x = 1.