Final answer:
The limit of the expression (4n² + 9)/(3n² + 7n + 11) as n approaches infinity is 4/3, determined by the ratio of the leading coefficients of the highest power terms in the numerator and denominator.
Step-by-step explanation:
The student asked what is the limit of the expression (4n² + 9)/(3n² + 7n + 11) as n approaches infinity. To find the limit of a rational function as n approaches infinity, we compare the degrees of the numerator and the denominator. Here, both the numerator and the denominator have the highest power of 2 (n²), so we look at the coefficients of this highest power term.
When n is very large, the lower-degree terms become insignificant. Thus, we simplify the limit to the ratio of the leading coefficients of the n² terms:
Limit as n approaches infinity of (4n² + 9)/(3n² + 7n + 11) = 4/3.