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Evaluate the limit lim_(n→∞)(n³-8)/(n³+8). What is its value?

1. (2)/(7)
2. (1)/(12)
3. (19)/(52)
4. None of these

Correct answer: None of these

Solution

As n approaches infinity, the dominant terms in the numerator and denominator are both n³. Thus, the limit simplifies to the ratio of the leading coefficients, which is 1. Therefore, the correct answer is 'None of these' since 1 is not listed as an option.

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