Find the limit: lim x➝0 sin | x | / 2x

We will use the concept of limits and function to find our required limit

Answer: The limit: lim x➝0 sin | x | / 2x does not exist.

Let's see how we will use the concept of limits and function to find our required limit.

Explanation:

For our limit that is lim x➝0 sin | x | / 2x ,

Let's take the left-hand limit first, that is, lim x➝0-. We are taking a point in the immediate vicinity of 0 but is negative.

Therefore , lim x➝0- sin (- x) / 2x = - lim x➝0- sin (x) / 2x = -1 

Let's take the right-hand limit first, that is, lim x➝0+. We are taking a point in the immediate vicinity of 0 but is positive.

Therefore , lim x➝0+ sin (x) / 2x = 1 

Now, we see that the left-hand limit is not equal to the right-hand limit.

Hence, the limit does not exist.