Example 19

Discuss the continuity of f ( x ) = Öx at x = 0

Solution : 1)

2)

3)

Therefore, f is continuous at x = 0 from right only.

Example 20

Discuss the continuity of f ( x ) =

Solution : 1) If we consider the interval ( - ¥ , - 4 ]

f ( x ) is not continuous at x = -4 from the left.

2) If we consider the interval [- 4, ¥ ) f ( x ) is not continuous

at x = - 4 from right.

Example 21

Discuss the continuity of f ( x ) = tan x on [ 0, p/2 ]

Solution : f ( x ) = tan x is continuous on ( 0, p/2 )

but not continuous at x = p/2 from the left.

Therefore f ( x ) = tan x is not continuous on [ 0, p/2 ].

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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