Question

I need help answering this practice problem for my calculus prep guide

Answer 1

The Solution:

Given the formula for the nth term of a sequence as below:

$\frac{8n^4-5}{6n^4+7}$

We are required to find the limit of the nth term as n tends to infinity.

$\lim _{n\to\infty}(\frac{8n^4-5}{6n^4+7})$

Step 1:

Divide each term by the highest denominator power.

$\lim _{n\to\infty}(\frac{\frac{8n^4}{n^4}^{}-\frac{5}{n^4}}{\frac{6n^4}{n^4}^{}+\frac{7}{n^4}})=\lim _{n\to\infty}(\frac{8^{}^{}-\frac{5}{n^4}}{6^{}^{}^{}+\frac{7}{n^4}})$

Step 2:

Substitute infinity for n, we have

$(\frac{8^{}-\frac{5}{\infty^4}}{6^{}+\frac{7}{\infty^4}})=(\frac{8^{}-0^{}}{6^{}+0^{}})=\frac{8}{6}=\frac{4}{3}$

Therefore, the correct answer is 4/3 [option 3]