We can see that the function approaches a particular value as x approaches `3` from the left:

x 2.5 2.6 2.7 2.8 2.9
f(x) 3.5 3.6 3.7 3.8 3.9

Continuing, we get closer and closer to `x = 3`:

x 2.9 2.92 2.94 2.96 2.97 2.98 2.99
f(x) 3.9 3.92 3.94 3.96 3.97 3.98 3.99

Likewise, approaching `x = 3` from the right gives the same limit value:

x 3.5 3.1 3.01 3.00001
f(x) 4.5 4.1 4.01 4.00001

We note that the function value is getting closer and closer to `4`.

We write:

`lim_(xrarr3)(x^2-2x-3)/(x-3)=4`

NOTE: We could have evaluated this limit by factoring first:

`lim_(xrarr3)(x^2-2x-3)/(x-3)`

`=lim_(xrarr3)((x+1)(x-3))/(x-3)`

`=lim_(xrarr3)(x+1)`

`=4`