Which of the following describes the limit of (4x^2+2x+1)/(3x^2 - x +5) as x→∞?

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Multiple Choice

Which of the following describes the limit of (4x^2+2x+1)/(3x^2 - x +5) as x→∞?

Explanation:
When x grows without bound, the highest-degree terms govern the limit. Here both the numerator and the denominator are quadratic, so divide by x^2 to compare: (4 + 2/x + 1/x^2) / (3 - 1/x + 5/x^2) As x → ∞, the terms with 1/x or 1/x^2 vanish, leaving 4/3. Therefore, the limit is 4/3.

When x grows without bound, the highest-degree terms govern the limit. Here both the numerator and the denominator are quadratic, so divide by x^2 to compare:

(4 + 2/x + 1/x^2) / (3 - 1/x + 5/x^2)

As x → ∞, the terms with 1/x or 1/x^2 vanish, leaving 4/3. Therefore, the limit is 4/3.

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