When we define instantaneous velocity we define it to be as the limit of average velocity. What actually this limit signify or what is limit?

The instantaneous velocity is given as

 

Here, the limit is taken for time interval. It has to tend to zero.

This limit signifies that the time interval for which the average velocity is measured is very small, that is, tending to zero.

 

Instantaneous velocity is the velocity at a particular instant of time, and hence the time interval needs to be very small. Hence, the limit is taken as ?t tending to zero.