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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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3.1 Continuity At a Point
3.2 Continuity In An Interval
3.3 Some Very -often - encountered Continuous Functions
3.4 Algebra Of Continuous Functions
3.5 Discontinuity And its Classification
3.6 Properties of Functions Continuous on an Interval

Chapter 4

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