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?
Continuous at x = 0 but discontinuous at x = 1
Continuous at x = 1 but discontinuous at x = 0
Continuous both at x = 1 and x = 0
Discontinuous both at x = 1 and x = 0
f0-=limn→∞ limn→0- cos2xn = a value lesser than 1∞=0f0+= limn→∞ limn→0+ 1+xn1n=1
Also, 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.