Final answer:
The limit of the function 6n^2+5 divided by 3n^2 as n approaches infinity is 2.
Step-by-step explanation:
The student is asking to evaluate the limit of the function 6n^2+5 divided by 3n^2 as n approaches infinity. To evaluate this limit, we note that the highest degree terms in both the numerator and the denominator are both n^2. We can divide both the numerator and the denominator by n^2 to simplify the expression.
\(\lim_{n \to \infty} \frac{6n^2+5}{3n^2} = \lim_{n \to \infty} \frac{6 + \frac{5}{n^2}}{3}\)
As n approaches infinity, \(\frac{5}{n^2}\) approaches 0, so the limit can be simplified to:
\(\lim_{n \to \infty} \frac{6 + 0}{3} = \frac{6}{3} = 2\)
Therefore, the limit exists and is equal to 2.