## Calculus (3rd Edition)

$f(x)=2\tan^{-1} x+\pi-2$ $g(x)=2\tan^{-1} (-x)+\pi-2$
Let's consider the functions $f(x)$ and $g(x)$: $f(x)=2\tan^{-1} x+\pi-2$ $g(x)=2\tan^{-1} (-x)+\pi-2$ We have: $\displaystyle\lim_{x\rightarrow-\infty} f(x)=-2$ $\displaystyle\lim_{x\rightarrow\infty} f(x)=4$ $\displaystyle\lim_{x\rightarrow -\infty} g(x)=4$ $\displaystyle\lim_{x\rightarrow\infty} g(x)=-2$ Therefore: $\displaystyle\lim_{x\rightarrow \infty} f(x)\not=\displaystyle\lim_{x\rightarrow \infty} g(x)$