# Limit of a Piecewise Function

In this tutorial we shall discuss the limit of a piecewise function. Let us consider an example of limit of piecewise function.

For what value of , exist, where

The given function is split into two parts, one is defined for and the other is defined for , so we have to take left hand and right hand limits. For left hand limit must approach 2 from left side, i.e. from the values less than 2 so left hand limit, we shall use the function part . Thus,

For right hand limit must approach 2 from right side, i.e. from the values greater than 2, so for right hand limit, we shall use the function part . Thus

It is given that the limit exists, so the left and right hand limits must be the same, i.e.