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

Estimate lim_(๐‘ฅโ†’โˆ’2) ๐‘“(๐‘ฅ) from the given table.

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Video Transcript

Estimate the limit as ๐‘ฅ tends to negative two of ๐‘“ of ๐‘ฅ from the given table.

In the table, weโ€™re given a selection of values of ๐‘ฅ and their corresponding values of ๐‘“ of ๐‘ฅ. For example, when ๐‘ฅ is negative 2.1, ๐‘“ of ๐‘ฅ is 36.9. We have to find the limit as ๐‘ฅ tends to negative two of ๐‘“ of ๐‘ฅ.

Notice that weโ€™re not given the value of ๐‘“ of negative two, but thatโ€™s okay because we donโ€™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 ๐‘“ of negative 2.001 is equal to 36.009 and ๐‘“ of negative 1.999 is equal to 35.991. Both values of the function are very close to 36. More than that, as ๐‘ฅ gets closer and closer to negative two from below, the value of ๐‘“ of ๐‘ฅ gets closer and closer to 36.

The same is true as ๐‘ฅ approaches negative two from above. ๐‘“ of negative 1.9 is 35.1, ๐‘“ of negative 1.99 is closer to 36 at 35.91, and ๐‘“ of negative 1.999 is even closer to 36 at 35.991.

Hence, we say that the limit as ๐‘ฅ tends to negative two of ๐‘“ of ๐‘ฅ is 36. As ๐‘ฅ approaches negative two both from below and from above, the value of ๐‘“ of ๐‘ฅ approaches 36.

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