3. Lim
x-infinity
x² +6x²+1/
x²+3
[AP]

Explanation:

Let n be the degree of the numerator

Let d be the degree of the denominator

If n < d, then the limit at infinity is always 0. This is because the denominator is growing faster compared to the numerator. I suggest looking at a table of values to see this in action.

In this case, n = 3 and d = 4, so we see that n < d is the case here. So that's why the answer is 0.

Side notes:

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.