# Math Help - complex limit question

1. ## complex limit question

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

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?

2. Originally Posted by transgalactic
$\lim_{y->\infty}=\frac{e^{-y}+e^{y}}{y-y^3}=\infty$

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?
Uh... $\frac{e^{-y}+e^y}{y+y^3}\geqslant\frac{e^y}{2y^3}$