Amath：found asymptote

lim(x->0) y = lim(x->0) (x^3+16)/4x
= lim(x->0) (x^2+4/x)
-> Infinity

Therefore a vertical asymptote is x=0

y = (x^3+16)/4x = (x^2+4/x)
lim(x->inf) y/x = lim(x->inf) (x^2+4/x)/x
= lim(x->inf) (x+4/x^2)
-> Infinity

Therefore there is no horizontal or oblique asymptote.

2013-05-26 13:44:33 補充：
If there is a horizontal asymptote, lim(x->inf) y = constant and lim(x->inf) y/x = 0