Mathematics Lab Activity-20 Class XI

Mathematics Laboratory Activities on Limits & Derivatives for class XI students Non-Medical. These activities are according to the CBSE syllabus

Chapter - 12 limits & Derivatives

Activity - 20

Objective

To find analytically   

Material Required

White paper , pencil, calculator. 

Theory

Procedure

1. Consider a function/given by:

              

At x = c = 3

2. The function given above is not defined at x = 3

3.   Take some values of x less than c = 3 and some other values of x more than   x = 3

4. In both cases, the values of x should be taken very close to c = 3.

5. Calculate the corresponding values of f(x) for values of x less than c = 3 but very close to c = 3  given in table 1 as shown below.

Table : 1

x	2.9	2.99	2.999	2.9999	2.99999	2.999999
f(x)	5.9	5.99	5.999	5.9999	5.99999	5.999999

Values of f(x) for values of x greater than c = 3 are given in table 2:

Table : 2

x	3.1	3.01	3.001	3.0001	3.00001	3.000001
f(x)	6.1	6.01	6.001	6.0001	6.00001	6.000001

Observations

It is clear from the above tables that:

1. Values of f(x) as x → 3 from the left, as in table 1 are coming closer and closer to 6.

2. Values of f(x) as x → 3 from the right, as in table 2 are coming closer and closer to 6, 

 

3. From table 1 and 2, we find that,

4. Also by using the formula we get

Result

Applications

This activity can be used to demonstrate the concept of   , when f(x) is not defined at x = c

VIVA – VOICE

Q. 1. What is the value of    ?

Ans. 1.

Q.2. What is the value of    ?

Ans. 1.

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