# How do you find all horizontal and vertical asymptotes of #f(x)=arctan x- 1/(x-1)#?

##### 1 Answer

Curvilinear asymptote :

Vertical asymptote:

Horizontal asymptotes:

#### Explanation:

The form

The first is a curvilinear asymptotes that has its outer asymptotes

See below the grandeur of the clustering, on either side of x = 1,

when general values are allowed to arc tan x. It is indeed marching

to

x = 1.

Here, the horizontal asymptotes are # y = (2 k + 1 ) pi/2, k = 0, +-1,

+-2 +-3, ...#.

These are the asymptotes of the curvilinear asymptotes

graph{(x - tan (y + 1 / ( x - 1 )))(x - 1) = 0[-2 3 -5 5]}