Question

Find the limit. Use I'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. lim

x→−[infinity]
​
(6x−ln(x))

Answer 1

Hi,

Explanation:

`\displaystyle \lim_(x \to \infty) (ln(x))/(x) =\frac{\infty} {\infty} \\\\So\ we\ can\ use\ Hospital's\ rule\\\\\lim_(x \to \infty) (ln(x))/(x)=\lim_(x \to \infty)((1)/(x) )/(1) =\lim_(x \to \infty)(1)/(x) =0\\`

`\displaystyle \lim_(x \to \infty) (6x-ln(x))=\lim_(x \to \infty) x(6-(ln(x))/(x) )\\\\=\lim_(x \to \infty)x*6=6*\infty=\infty\\`