let f(x) = ((tanx)/(tan2x)) . Find the points of discontinuity of f on [0,2π] and determine wether each duscontinuity is a point discontinuity,a jump discontinuity,or a vertical asymtote


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Question Number 73569 by Rio Michael last updated on 13/Nov/19

$l e t f (x) = \frac{t a n x}{t a n 2 x} . F i n d t h e p o i n t s o f d i s c o n t i n u i t y$ $o f f o n [0, 2 π] a n d d e t e r m i n e w e t h e r e a c h d u s c o n t i n u i t y i s$ $a p o i n t d i s c o n t i n u i t y, a j u m p d i s c o n t i n u i t y, o r a v e r t i c a l a s y m t o t e$
Commented by Rio Michael last updated on 13/Nov/19

$i a p p r e c i a t e$
Commented by kaivan.ahmadi last updated on 13/Nov/19

$f (x) = \frac{\frac{s i n x}{c o s x}}{\frac{s i n 2 x}{c o s 2 x}} = \frac{s i n x c o s 2 x}{c o s x s i n 2 x}$ $c o s x = 0 \Rightarrow x = \frac{π}{2}, \frac{3 π}{2}$ $s i n 2 x = 0 \Rightarrow x = 0, \frac{π}{2}, π$ $\Rightarrow f i s n o t c o n t i n u o u s a t {0, \frac{π}{2}, \frac{3 π}{2}, π} .$
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