If

$$f$($x$)$equalsStartFraction p left parenthesis x right parenthesis Over q left parenthesis x right parenthesis EndFraction

for polynomials$$ p$($x$)$ and$$ q$($x$),$

ModifyingBelow lim With x right arrow infinity$$f$($x$)$

can be found by dividing$$ p$($x$)$ and$$ q$($x$)$ by the

$$

$$

power of x in

$$

$$

p$($x$)$

q$($x$)$

and then using the rules for$$ limits$,$ including the rule for limits at$$ infinity,

$$

$$

ModifyingBelow lim With x right arrow plus or minus infinity StartFraction $1$ Over x Superscript n EndFraction equals $0$

ModifyingBelow lim With x right arrow plus or minus infinity StartFraction $1$ Over x Superscript n EndFraction equals $1$

ModifyingBelow lim With x right arrow plus or minus infinity StartFraction $1$ Over x Superscript n EndFraction equals plus or minus infinity

$,$

for any positive real number$$ n$,$ to find the limit$.$