HOW TO FIND A LIMIT USING A TABLE

Here we are going to see how to find a limit using a table.

First let us understand what is limit.

Let I be an open interval containing x∈ R.

Let f : I ---> R. Then we say that the limit of f(x) is L, as x approaches x0 [Usually written as limx--->0f(x) = L]. Whenever x becomes sufficiently close to x0 from either side with x ≠ x0, f(x) gets sufficiently close to L.

In the following examples, complete the table using calculator and use the result to estimate the limit.

Example 1 :

calculatelimitusingtable1.png

Solution :

Substitute the values of x from the table above into f(x).

When x = 1.9,

When x = 1.99,

When x = 1.999,

When x = 2.001,

When x = 2.01,

When x = 2.1,

From the above table, we have to estimate the limit when x tends to 2.

Here x--->2 appears between 1.999 to 2.001. By observing the table, we may estimate the limit as 0.333.....

Example 2 :

Solution :

Substitute the values of x from the table above into f(x).

When x = 1.9,

When x = 1.99,

When x = 1.999,

When x = 2.001,

When x = 2.01,

When x = 2.1,

Here x--->2 appears between 1.999 to 2.001. By observing the table, we may estimate the limit as 0.25.

Example 3 :

calculatelimitusingtable3.png

Solution :

When x = -0.1,

When x = -0.01,

When x = -0.001,

When x = 0.001,

When x = 0.01,

When x = 0.1,

Here x--->0 appears between -0.001 to 0.001. By observing the table, we may estimate the limit as 0.288.....

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