How do you find the vertical, horizontal and slant asymptotes of: #tan(x)#?

1 Answer
Jul 25, 2016

Answer:

Only vertical asymptotes #x = (2n+1)pi/2, n = 0. +-1, +-2, +-3, ...#, in both positive and negative directions of y=axis.

Explanation:

y = tan x is periodic with period #pi#

As # x to (2n+1)pi/2+-, n = 0, +-1, +-2, +-3, ...#,

#x to -+ oo#.

#(2n+1)pi/2+-# is used to indicate the limits,

for approach from higher and lower values, respectively.

So, the graph is asymptotic with

#x = (2n+1)pi/2, n = 0, +-1, +-2, +-3, ...,#3

in both positive and negative directions of y-axis