Evaluate lim (x -> infinity) [ (4x^3 - 2x + 1) / (7x^3 + 5x^2 - 3) ].
Answer and explanation
Correct answer: A. 4/7
- Step 1: Divide all terms in numerator and denominator by the highest power of x, which is x^3.
- Step 2: lim (x -> infinity) [ (4 - 2/x^2 + 1/x^3) / (7 + 5/x - 3/x^3) ] = (4 - 0 + 0) / (7 + 0 - 0) = 4/7.
Answer
4/7.
Why not the others: '0' applies when the denominator has a higher degree; 'infinity' applies when the numerator has a higher degree; '-1/3' is the ratio of constant terms.
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