Let n be the least integer such that f(x) is O(xⁿ). Arrange the following functions in increasing order of n: A. f(x) = 3x³ + (log x)⁴ B. f(x) = (x⁵ + x² + 1)/(x³ + 1) C. f(x) = (x³ + x² + 1)/(x² + 1) D. f(x) = (x² + 5 log x)/(x² + 1)

1. AD, C, A, B
2. BD, C, B, A
3. CB, C, A, D
4. DB, A, C, D

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Correct answer: B. D, C, B, A

Explanation

A grows like x³ (n = 3); B like x² (n = 2); C like x (n = 1); D tends to a constant (n = 0). Increasing order: D, C, B, A.