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

Aug 25, 2016

$= 0$

#### Explanation:

${\lim}_{x \to \infty} \sinh \frac{2 x}{e} ^ \left(3 x\right)$

$= {\lim}_{x \to \infty} \frac{{e}^{2 x} - {e}^{- 2 x}}{2 {e}^{3 x}}$

$= {\lim}_{x \to \infty} \frac{{e}^{- x} - {e}^{- 5 x}}{2 {e}^{0}}$

$= {\lim}_{x \to \infty} \frac{{e}^{- x} - {e}^{- 5 x}}{2}$

$= \frac{{\lim}_{x \to \infty} {e}^{- x} - {e}^{- 5 x}}{2}$

$= 0$