Question

How do you determine the limit of `sinh(2x)/e^(3x)` as x approaches infinity?

Answer 1

`= 0`

Explanation:

`lim_(x to oo) sinh(2x)/e^(3x)`

`= lim_(x to oo) (e^(2x) - e^(-2x))/(2e^(3x))`

`= lim_(x to oo) (e^(-x) - e^(-5x))/(2e^(0))`

`= lim_(x to oo) (e^(-x) - e^(-5x))/(2)`

`= (lim_(x to oo)e^(-x) - e^(-5x))/(2)`

`= 0`