text: why are limits to infinity considerably important?   limits to infinity can give you the upper or lower bound of a function.  in other words they can give you a horizontal asymptote for the graph of a function.  it will tell you that a quantity will get no higher (or lower) than this value.  also, limits to infinity are used to compute infinite integrals.  an amazing example is the area between the graph of y = e^(-x) from x=0 to infinity and the x-axis.  you might think that the area is infinite since the x values go from 0 to infinity, but actually the answer is 1 sq. unit.