3.5 Discontinuity And Its Classification
A function f(x) is said to be discontinuous for the point x
= c if at least one of three numbers f(c),
is different from the other two roughly we have the following types
^{
}
^{ }(a) If x = c and if
the point is said to have
ordinary or finite discontinuity
(b) If
then ’f’ has ordinary discontinuity on the right.
Similarly if f(c) = lim f(x) but lim f(x, then ’f’
has ordinary discontinuity on the left.
(c) If then ’f’ has removable discontinuity at x = c.
^{ }The function ’f’ is made continuous at
x = c by assigning
We shall now illustrate the different types of
discontinuities by using examples.
Consider a function f(x) and a point P whose abscissa is
x = c; then following cases may arise.
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