Notice that: lim x → ∞ x = ∞ {\displaystyle \lim _{x\to \infty }x=\infty } Also, we have that: lim x → ∞ log ( x + 1 x ) = log ( 1 ) = 0 {\displaystyle \lim _{x\to \infty }\log({\frac {x+1}{x}})=\log(1)=0} . This justifies our use of L'Hospital's rule.
