Compute the value of the following limit.

Solution: Notice as well that I did say estimate the value of the limit.  Again, we will not directly compute limits in this section. The point of this section is to give us a better idea of how limits work & what they can tell us regarding the function.

We will select values of x that get closer and closer to x=2 & plug these values into the function.  Doing this gives the following table of values.

Note that we ensured & picked values of x that were on both sides of x = 2 to ensure that any trends which we might be seeing are x =2 and which we moved in extremely close to actually correct.

Also notice as well that we can't in fact plug in x = 2 into the function as it would give us a division by zero error.  It is not a problem as the limit doesn't care what is happening at the point in question.

From given table it appears that the function is 4 as x approaches 2, so

Let's think a little bit more about what's going on here.  Let's graph the function from the last example.  The graph of the function in the range of x's that were interested in is shown below.