Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2008 / Paper 1 / 19 / a / ii / Solution

For $n=1,2,3$ the limit zero equals the assigned value at zero. For $n=4$ the limit is zero but the assigned value is one, giving a removable discontinuity. For $n=0$ there is no limit. Thus continuity at zero holds precisely for