Here is the expression .
In:= t = Sin[x]/x
If you replace x by 0, the expression becomes 0/0, and you get an indeterminate result.
In:= t /. x->0
If you find the numerical value of for close to , however, you get a result that is close to .
In:= t /. x->0.01
This finds the limit of as approaches . The result is indeed .
In:= Limit[t, x->0]