Chapter 7.3, Problem 92E

(a)

To determine

To sketch: The graph of $l\left(x\right)=x$ and $f\left(x\right)=x\tanh x$ then show that $l\left(x\right)=x$ is slant asymptotes of $f\left(x\right)=x\tanh x$. and check out that, does f have any other slant asymptotes is possible.

(b)

To determine

To show: The function $f\left(x\right)=x\tanh x$ to behave like $l\left(x\right)=x$. as x gets large.

(c)

To determine

To prove: The slant asymptote of $f\left(x\right)=x\tanh x$ is $l\left(x\right)=x$ by confirming $\underset{x\to \infty }{\lim }\left(x\tanh x-x\right)=0$.