Example:

Consider a factory that produces defense equipment. Assume that the production cost depends on a single parameter t. So, let the production cost function be P(t) = 2t. Also, assume that the number of units produced is a function of t. Let the function for the number of units produced be U(t) = t² + 2. The factory management is interested in knowing the cost per unit of the equipment produced in the factory. So, the cost per unit function, C(t), is obtained by dividing P(t) by U(t). The table below indicates the total production cost function, the number of units produced function, and the cost per unit function for various values of t.

We can see from the table that as the value of t increases, the value of U(t) increases sharply when compared to the value of P(t). The increase in the value of the function U(t) cannot be compensated by the increase in the value of the function P(t). In other words, P(t) can be ignored for large values of t. Thus, we can say that as the value of t tends to infinity, the value of the function tends to 0. A graph for C(t) versus t is shown below.

We write

if the functional value f(x) is close to the single real number A whenever x is close to but not equal to c on either side of c.