This continuity is called Isolated point discontinuity and it can be removed by assigning f(1) = 2
Example 13 Consider f(x) = sin
, x ¹0
= 0 when x = 0
we know that lim sin
DNE. In fact sin
oscillates between 1 and 1 as x®0
from either side. Hence x = 0 is a point of finite oscillatory
discontinuity
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