let-f-x-tanx-tan2x-Find-the-points-of-discontinuity-of-f-on-0-2pi-and-determine-wether-each-duscontinuity-is-a-point-discontinuity-a-jump-discontinuity-or-a-vertical-asymtote-

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} .