# Does the limit #lim_(x->3) (f(x)-f(3))/(x-3)# always exist?

##### 2 Answers

Kindly refer to the **Discussion** given in the **Explanation.**

#### Explanation:

The **Limit** under reference **may or may not exist.**

Its **existence** depends upon the **definition of the function**

Consider the following **Examples :**

Clearly, the **Limit** =

We find that, **exists,** and, **is**

Remember that,

Since,

On the other hand, as

We conclude that, **does not exist.**

**Enjoy Maths.!**

Recall the limit definition of the derivativbe, that is:

# f'(a) = lim_(x rarr a) (f(x)-f(a))/(x-a)#

We have:

# L = lim_(x->3) (f(x)-f(3))/(x-3)#

And so clearly:

# L = f'(3) #

Without further knowledge of the function we cannot determine if the limits exist. If it were known that