**Velocity of the Body**

To calculate the velocity of the body within the error limit, we need to divide the distance traveled by the time taken. The velocity is given by the formula:

Velocity = Distance / Time

Given:
Distance = (13.8 - 0.2)m
Time = (4.0 - 0.3)s

**Calculating the Distance and Time with Error Limits**

To consider the error limits, we need to calculate the maximum and minimum values of distance and time.

Maximum Distance = 13.8m + 0.2m = 14.0m
Minimum Distance = 13.8m - 0.2m = 13.6m

Maximum Time = 4.0s + 0.3s = 4.3s
Minimum Time = 4.0s - 0.3s = 3.7s

**Calculating the Maximum and Minimum Velocity**

Now, we can calculate the maximum and minimum velocity by dividing the maximum and minimum distances by the maximum and minimum times, respectively.

Maximum Velocity = Maximum Distance / Minimum Time
= 14.0m / 3.7s
= 3.7838 m/s (rounded to four decimal places)

Minimum Velocity = Minimum Distance / Maximum Time
= 13.6m / 4.3s
= 3.1628 m/s (rounded to four decimal places)

**The Velocity Within Error Limit**

The velocity of the body within the error limit can be expressed as a range between the maximum and minimum velocities.

Velocity Range = Minimum Velocity - Maximum Velocity
= 3.1628 m/s - 3.7838 m/s
= -0.6210 m/s (rounded to four decimal places)

The negative value indicates that there is an error in the calculation, and the velocity cannot be negative. Therefore, the velocity within the error limit is between 3.1628 m/s and 3.7838 m/s.

**Explanation**

In this problem, we are given the distance traveled by a body and the time taken, along with their error limits. By considering the maximum and minimum values of distance and time, we can calculate the maximum and minimum velocities. The velocity within the error limit is then determined by finding the range between the minimum and maximum velocities. In this case, the velocity is found to be between 3.1628 m/s and 3.7838 m/s.