Estimate the limit as 𝑥 tends to negative two of 𝑓 of 𝑥 from the given table.
In the table, we’re given a selection of values of 𝑥 and their corresponding values of 𝑓 of 𝑥. For example, when 𝑥 is negative 2.1, 𝑓 of 𝑥 is 36.9. We have to find the limit as 𝑥 tends to negative two of 𝑓 of 𝑥.
Notice that we’re not given the value of 𝑓 of negative two, but that’s okay because we don’t need it. To find the limit of a function at a particular point, we just need the values of that function at near the point.
We can see that the value of 𝑓 of negative 2.001 is equal to 36.009 and 𝑓 of negative 1.999 is equal to 35.991. Both values of the function are very close to 36. More than that, as 𝑥 gets closer and closer to negative two from below, the value of 𝑓 of 𝑥 gets closer and closer to 36.
The same is true as 𝑥 approaches negative two from above. 𝑓 of negative 1.9 is 35.1, 𝑓 of negative 1.99 is closer to 36 at 35.91, and 𝑓 of negative 1.999 is even closer to 36 at 35.991.
Hence, we say that the limit as 𝑥 tends to negative two of 𝑓 of 𝑥 is 36. As 𝑥 approaches negative two both from below and from above, the value of 𝑓 of 𝑥 approaches 36.