Example 24

Discuss the continuity, of function f defined by

f ( x ) = , 2 £ x < 5

ii) Let c Î ( 2, 5 )

f ( c ) = .

\ f is continuous at x = c and hence in ( 2, 5 )

Thus ’ f ’ is continuous in [ 2, 5 ) i.e. f is continuous in the open

interval ( 2, 5, ) and continuous only from right at x = 2.

Example 25

Discuss the continuity of the function f defined by

f ( x ) = Ö( x - a ) ( x - b ) for a £ x £ b

Solution : If x ³ a and x £ b, f ( x ) becomes real. If x < a or x > b.

f ( x ) is not real. We, therefore, examine the continuity on [ a, b ]

Let c Î ( a, b )

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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