Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.8 Exercises - Page 390: 17

$\displaystyle \lim_{x\rightarrow\infty}\sinh x=\infty$

$\displaystyle \sinh x=\frac{e^{x}-e^{-x}}{2}$ When $x\rightarrow\infty ,\qquad e^{x}\rightarrow\infty,\quad e^{-x}\rightarrow 0$ $\displaystyle \lim_{x\rightarrow\infty}\sinh x=\infty$