Discussion
The value of \(\lim_{n \to \infty} \frac{3n^{2}+5n+4}{4+2n^{2}}\) is
Answer: C
The limit is 1.5.
Divide the numerator and denominator by \(n^{2}\), the highest power:
\[ \frac{3 + 5/n + 4/n^{2}}{4/n^{2} + 2} \to \frac{3}{2} = 1.5 \]
For a ratio of polynomials of equal degree, the limit is the ratio of the leading coefficients. 0 would need the denominator to be of higher degree. 0.75 is \(\frac{3}{4}\), dividing by the constant term 4 instead of the coefficient 2. 3 ignores the denominator's coefficient.
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