2. Continuity
A function is said to be continuous at x = a
if there is no interruption in the graph of
f(x) at a. Its graph is unbroken at a, and
there is no hole, jump or gap.
3. Continuity of a function at a point
A function is said to be continuous at a point
x = a if the following three conditions are
satisfied:
1. f(x) is defined, that is, exists, at x = a
2. The limit of f(x) as x approaches a exists
3. The limit of f(x) as x approaches a is
equal to f(a).
6. Removable Discontinuity
A function is said to have removable
discontinuity at x =a, if the limit of f(x) as x
approaches a exists, and is not equal to
f(a)
8. Jump Discontinuity
A function is said to have jump
discontinuity at x =a, if the limit of f(x)
as x approaches to a from the right is
not equal to the limit of f(x) as x
approaches to a from the left.