Chapter 6.9, Problem 55ES

In parts (a)-(f) find the limits, and confirm that they are consistent with the graphs in Figures $\mathrm{6.9.1}$ and $\mathrm{6.9.6}$ .

(a) $\underset{x\to +\infty }{\lim }\sinh x$

(b) $\underset{x\to -\infty }{\lim }\sinh x$

(c) $\underset{x\to +\infty }{\lim }\tanh x$

(d) $\underset{x\to -\infty }{\lim }\tanh x$

(e) $\underset{x\to +\infty }{\lim }{\sinh }^{-1}x$

(f) $\underset{x\to 1^{-1}}{\lim }{\tanh }^{-1}x$