spring 2020 test main sitting question 2

[bnogas]

On page 2 of the spring 2020 tests solutions, there is the following question and solution and associated solution. How do we find the limit of n(n^2+1)^2/3(n+1)((n+1)^2 + 1)^2

[Maria-Clara Eberlein]

Without actually expanding the numerator and denominator, you can see that they would have the same degree (5) and so the limit is the leading coefficient of the numerator (1) divided by the leading coefficient of the denominator (3), so 1/3.