We have a graph with a discontinuity and we want to obtain the limit as x tends to 3.
The catch here is that since the function is discontinuous ( is not smooth at 3),
There are 2 limits, one coming from the left and one coming from the right.
We also have the value that the function assumes at 3, which is 7.
Thus, the limit.
[tex]\text{Lim}_{x\rightarrow3^-}f(x)[/tex]This reads, the limit of f(x) at x = 3 coming from the left side ( that's what the 3 minus means).
If we come to the discontinuity at 3, from the left ( x --> 3 minus) f(x) "approaches" 1 ( it approaches 1, it isn't 1 really, it is 7).
If we were coming from the right side the function would approach 3.
It looks weird that the function looks like it has 3 values at x = 3, but it has only 1.
Therefore
[tex]\text{Lim}_{x\rightarrow3^-}f(x)=1[/tex]
