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.

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