Consider the function f(x) = 2x + 3 and we want to find the limit of this function at x = 1.

Explanation

Let us complete the value of the function for value of x very near to 1.
First we consider values of x approaching 1 from the left i.e., `x lt 1`
`{:(x,0.5,0.7,0.8,0.9,0.95,0.99),(f(x) = 2x + 3,4,4.4,4.6,4.8,4.9,4.98):}`
Now, we consider values of X approaching 1 from the right ie `x gt 1`
`{:(x, 1.0001,1.001,1.01,1.05,1.1,1.2),(f(x)=2x + 3,5.0002,5.002,5.02,5.1,5.2,5.4):}`
From both the tables, we observe that value of f(x) at x = 1 should be greater than 4.98 than and less than 5.0002
So, it is reasonable to assume that value of f(x) at x = 1 as dictated by the numbers to the left of 1 is 5
i.e., `underset(x to 1)(lim f(x) = 5`
Similarly, when x approaches 1 form the right, f(x) should be taking value 5 i.e.,
`underset(x to 1) f(x) = 5`
Hence, the left hand limit of f(x) and right and limit of f(x are both equal to 5.
Thus, `underset(x to 1)(lim) f(x) = underset(x to 1)(lim) f(x) = underset(x to 1)(lim) f(x) = 5`
This can be explained with the help of graph also