Learn Find The Limit Lim X 0 Sin X X

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

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

## Answer: The limit 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 | / x ,

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) / x = - lim x➝0- sin (x) / x = -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) / x = 1

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

### Hence, the limit does not exist.

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