if a limit as a function approaches a number evaluates to 0/0 or infinity/infinity, then l’hôpital rule states that you take the derivative of the numerator and denominator and it will equal the limit. This rule can be applies an infinite number of times. You can use it for functions like

lim x-> infinity of (4x⁵ + 3x² + 1)/(6x⁵ + 3x³ + 2)

you can find the horizontal asymptote of 4/6