How do you find the limit of $tan x$ $tanx$ as $x \to π$ $x->pi$ ?

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Answer 1 · 2018-03-03T12:49:55

$lim_(x->pi) tan(x)=0$

This limit can be evaluated by simply substituting in $pi$ since $tan$ is continuous and defined at $pi$ :

$lim_(x->pi) tan(x)=tan(pi)$

In case we have forgotten the value of $tan(pi)$ , we can use the following identity to figure it out:
$tan(theta)=sin(theta)/cos(theta)$

This gives:
$tan(pi)=sin(pi)/cos(pi)=0/(-1)=0$

How do you find the limit of tanxtanxtanx as x->pix→πx->pi?