Evaluate the limit: lim (x -> infinity) [(3x^2 - 5x + 2) / (7x^2 + 4x - 1)].
Answer and explanation
Correct answer: B. 3/7
- Step 1: This is an indeterminate form of type infinity / infinity with polynomials of equal degree (degree 2).
- Step 2: Divide numerator and denominator by the highest power x^2: lim [(3 - 5/x + 2/x^2) / (7 + 4/x - 1/x^2)].
- Step 3: As x -> infinity, all terms with 1/x and 1/x^2 approach 0, leaving 3/7.
Answer
3/7.
Why not the others: '0' would be correct if the denominator degree were higher than the numerator; 'infinity' would be correct if the numerator degree were higher; '-2' takes the ratio of the constant terms.
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