As an application of theorems 5.2.3 and 5.2.5, it follows that the function defined by is continuous.
5.2 .7
Note:
Geometrically, saying that a function is continuous on the interval, means that there is no break in the graph of the function, we can draw its graph on paper starting with to without lifting the pen.
Practice Exercises 5.2 : Continuity of a function
(1) Discuss the continuity of the following functions :
(i)
(ii)
(iii)
(2) Discuss continuity of at x = 2, where is such that for all and is continuous on
(3) Letbe continuous function such that in every neighbourhood of 0, there exists a point where
, then 
is continuous at 
. 
defined by
is continuous. 
is continuous on the interval, means that there is no break in the graph of the function, we can draw its graph on paper starting with 
to 
without lifting the pen.
at x = 2, where 
is such that 
for all 
and is continuous on 
be continuous function such that in every neighbourhood of 0, there exists a point where 
