limit of cosh and sinh

[azreal]

I want to show that for all \(\displaystyle k \in \mathbb{N}\)
\(\displaystyle \lim_{t \rightarrow \infty} t^{-k} cosh(t) = \lim_{t \rightarrow \infty} t^{-k} sinh(t) = \infty \)
I've tried to use the definition of cosh and sinh, but this didn't get my very far...

 

[stapel]

I want to show that for all \(\displaystyle k \in \mathbb{N}\)
\(\displaystyle \lim_{t \rightarrow \infty} t^{-k} cosh(t) = \lim_{t \rightarrow \infty} t^{-k} sinh(t) = \infty \)
I've tried to use the definition of cosh and sinh, but this didn't get my very far...

How far did you get? Please show your working. Thank you!