Question

The nth term of a sequence is represented by 3n4−10/6n4+7 . What is the limit of the the nth term as n becomes increasingly large?

Answer 1

Answer:

1/2

Step-by-step explanation:

Given the limit of the function expressed as;

$\lim_{n \to \infty} \frac{3n^4-10}{6n^4+7}$

To take the limit, we nee to divide through by the highest power of n first

$\lim_{n \to \infty} \frac{3n^4/n^4-10/n^2}{6n^4/n^4+7/n^4}\\= \lim_{n \to \infty} \frac{3-10/n^2}{6+7/n^4}\\= \frac{3-10/(\infty)^2}{6+7/(\infty)^4}\\= \frac{3-0}{6-0}\\= \frac{3}{6}\\ = \frac{1}{2}$

Hence the limit of the the nth term as n becomes increasingly large is 1/2