The nth term of a sequence is represented by 8n^4-5/6n^4+7. What is the limit of the the nth term as x becomes increasingly large?

313

34

43

The limit of the nth term does not exist.

4/3

Step-by-step explanation:

lim (n→∞) (8n⁴ - 5) / (6n⁴ + 7)

To find the limit, compare the orders (highest exponents) of the numerator and denominator.

If the order of the numerator is bigger, the limit does not exist.

If the order of the denominator is bigger, the limit is 0.

If the orders are equal, the limit is the ratio of the leading coefficients.

Here, both the numerator and denominator have order 4, so the limit is 8/6, which reduces to 4/3.