Chapter 3.11, Problem 23E

(a)

To determine

To find: $\underset{x\to \infty }{\lim }\tanh x$ by using definition of the hyperbolic function.

(b)

To determine

To find: $\underset{x\to -\infty }{\lim }\tanh x$ by using definition of the hyperbolic function.

(c)

To determine

To find: $\underset{x\to \infty }{\lim }\sinh x$ by using definition of the hyperbolic function.

(d)

To determine

To find: $\underset{x\to -\infty }{\lim }\sinh x$ by using definition of the hyperbolic function.

(e)

To determine

To find: $\underset{x\to \infty }{\lim }\mathrm{sech}x$ by using definition of the hyperbolic function.

(f)

To determine

To find: $\underset{x\to \infty }{\lim }\coth x$ by using definition of the hyperbolic function.

(g)

To determine

To find: $\underset{\begin{array}{l}x\to 0-\\ x\to 0\end{array}}{\lim }\coth x$ use definition of the hyperbolic function.

(h)

To determine

To find: $\underset{\begin{array}{l}x\to 0-\\ x\to 0\end{array}}{\lim }\coth x$ use definition of the hyperbolic function.

(i)

To determine

To find: $\underset{x\to -\infty }{\lim }\mathrm{csch}x$ by using definition of the hyperbolic function.

(j)

To determine

To find: $\underset{x\to \infty }{\lim }\frac{\sinh x}{e^x}$ use definition of the hyperbolic function.