$\displaystyle \lim_{y->\infty}=\frac{e^{-y}+e^{y}}{y-y^3}=\infty$

i cant see how to prove that it goes infinity

one way of thinking is:

the numerator growes faster then the denominator

the other is if we break e^x into taylor series

an devide by the denominator and the result goes to infinity

is there other way of proving the result?