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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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Index

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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