Page 39 - Mathematics Class - XII

ACTIVITY 3.3

OBJECTIVE
To find analytically the limit of a function f (x) at x = c and also check the continuity of the function at that point.

MATERIAL REQUIRED

Y Paper Y Pen
Y Pencil Y Calculator

PRE-REQUISITE KNOWLEDGE

1. Knowledge of the concept, the limit of a function at a point.
2. Knowledge of the concept, the continuity of a function at a point.

PROCEDURE

1. Consider the function f (x), given by

x 25
2
fx() , x
5
x 5

10 , x 5
2. Take some points on the left and some points on the right side of c (= 5) which are very close to c.

3. Find the corresponding values of f (x) for each of the points considered in Step 2 above as:

2
fx() x 25
x 5
x ( 5 )( x 5 ) x ( 5 as x 5
),
x 5
4. Record the values of points on the left and right side of c as x and the corresponding values of f (x) in the
form of a table.

DEMONSTRATION

1. The values of x and f (x) are recorded as follows:

Table 1: For points on the left of c (= 5):–

x 4.9 4.99 4.999 4.9999 4.99999 4.999999 4.9999999

f (x) 9.9 9.99 9.999 9.9999 9.99999 9.999999 9.9999999

37