Question Video: Finding the Limit of a Function from a Table Mathematics • Higher Education

Estimate lim_(π‘₯β†’βˆ’2) 𝑓(π‘₯) from the given table.

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Video Transcript

Estimate the limit as π‘₯ tends to negative two of 𝑓 of π‘₯ from the given table.

In the table, we’re given a selection of values of π‘₯ and their corresponding values of 𝑓 of π‘₯. For example, when π‘₯ is negative 2.1, 𝑓 of π‘₯ is 36.9. We have to find the limit as π‘₯ tends to negative two of 𝑓 of π‘₯.

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 π‘₯ gets closer and closer to negative two from below, the value of 𝑓 of π‘₯ gets closer and closer to 36.

The same is true as π‘₯ 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 π‘₯ tends to negative two of 𝑓 of π‘₯ is 36. As π‘₯ approaches negative two both from below and from above, the value of 𝑓 of π‘₯ approaches 36.

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