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Dividing numerator and denominator by n2, we have lim n → [infinity] 3 11n2 n 14n2 = lim n → [infinity] 3 11n2 n2 n 14n2 n2 = lim n → [infinity]

Answer :

Final answer:

The limit is 3/14.

Explanation:

To evaluate the given limit, we employ the technique of dividing both the numerator and the denominator by the highest power of n, which in this case is n^2. This step simplifies the expression and allows us to apply the limit properties. By dividing both the numerator and denominator by n^2, we obtain a new expression where the highest power of n is in the denominator, which facilitates the evaluation of the limit.

After dividing both the numerator and denominator by n^2, the expression transforms into a simpler form. This manipulation helps us analyze the behavior of the expression as n approaches infinity. Dividing by n^2 in both the numerator and the denominator results in canceling out the common terms involving n^2, leading to a simpler expression that retains the essence of the original one.

As n approaches infinity, the limit of the simplified expression can be directly determined. The simplified expression becomes more manageable, and we can easily evaluate the limit. In this case, after dividing by n^2, the limit converges to 3/14 as n tends to infinity. Therefore, the correct option is the limit is 3/14.

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