Page 89 - Mathematics Class - XI

Unit IV Calculus
Calculus

TOPIC - 12: Limits and Derivatives

ACTIVITY 12.1

OBJECTIVE
x − c 2
2
To find analytically lim( )fx =
−
x→ c xc
MATERIAL REQUIRED
 White paper

 Pen/Pencil

 Calculator

PRE-REQUISITE KNOWLEDGE

1. Knowledge of functions

2. Knowledge of limits

PROCEDURE
x − 16
2
1. Consider the function f given by f(x) = .
−
x 4
2. In this case, c = 4 and the function is not defined at x = 4.

DEMONSTRATION

1. Take some values of c less than 4 and some other values of c more than 4.
2. In all cases, the values to be taken have to be very close to 4.

3. Calculate the corresponding values of f at each of the values of c taken close to 4.

Write the values of f(x) in the following tables:

Table 1 [Values of f(x) at some values of c less than 4]

x 3.9 3.99 3.999 3.9999 3.99999 3.999999

f(x) 7.9 7.99 7.999 7.9999 7.99999 7.999999

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