Answer
The function converges to 2
Work Step by Step
Evalute the improper integral
$\int ^{\infty}_1 \frac{6}{x^4}dx $
The function is continuous on the interval, rewrite with a limit
$ \lim\limits_{b \to \infty} \int ^b_1 \frac{6}{x^4}dx$
$\lim\limits_{b \to \infty} [-2x^{-3}]^b_1$
$\lim\limits_{b \to \infty} [(-2b^{-3}) - (-2)] $
evaluate b at infinity
$ -\frac{2}{\infty} +2$
$0 +2$
2
The function converges to 2 as it goes to infinity
