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

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Answer 1 · 2016-07-25T03:03:59

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

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

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