Question

Find the asymptote equations:
f(x)=(x^3+2)/(x^4+1)

Answer 1

there are no vertical asymptotes since f is continuous for all x


we can divide out x^3 leaving
\[f(x) = (1+2/x ^{3})/(x +1/x ^{3})\]
then let x -> infinity
f(x) -> 1/x ->0

so we have a horizontal asymptote at f(x)=0 or y=0