Question Video: Finding the Limit of a Function from a Table Mathematics • 12th Grade

Estimate lim_(π₯ββ2) π(π₯) from the given table.

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Video Transcript

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

In the table, weβre given a selection of values of π₯ and their corresponding values of π of π₯. For example, when π₯ is negative 2.1, π of π₯ is 36.9. We have to find the limit as π₯ tends to negative two of π of π₯.

Notice that weβre not given the value of π of negative two, but thatβs okay because we donβ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 π of negative 2.001 is equal to 36.009 and π 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 π of π₯ gets closer and closer to 36.

The same is true as π₯ approaches negative two from above. π of negative 1.9 is 35.1, π of negative 1.99 is closer to 36 at 35.91, and π 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 π of π₯ is 36. As π₯ approaches negative two both from below and from above, the value of π of π₯ approaches 36.