Page 201 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes 7.1.2 Limit of a Difference Quotient

Example: Difference quotient of a function f is given by

2

If f(x) = x , find .
Solution:

=

=

=

=

7.1.3 Laws of Limits

Calculating limits using graphs and tables takes a lot of unnecessary time and work. Using the
limit laws listed below, limits can be calculated much more quickly and easily.
Let and exist and let c be a constant.

1.

2.

3.

4.

5.

6.

The following properties are special limit laws:
7.

8.

From the limit laws above, comes the property of direct substitution. This property makes it
possible to solve most rational and polynomial functions. The property of direct substitution
states: For any rational or polynomial function f, if a is in the domain of f then
= f(a)

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