MHB Finding the Continuous Intervals for a function

[cbarker1]

I need some help find some continuous intervals for $f(x)=tan(2x)$. I know there are vertical asympotes when x=pi/4+2*pi*n for positive integers. Thank you for your help.

CBarker1

 

[evinda]

I need some help find some continuous intervals for $f(x)=tan(2x)$. I know there are vertical asympotes when x=pi/4+2*pi*n for positive integers. Thank you for your help.

CBarker1

$f(x)=tan(2x)$ is continuous everywhere except the vertical asymptotes. To find the vertical asymptotes,we set the denominator $0$.So,as $tan(2x)=\frac{sin(2x)}{cos(2x)}$,we set $cos(2x)=0 \Rightarrow x=\pm \frac{\pi}{4},\pm \frac{3\pi}{4},...$
Therefore,$tan(2x)$ is continuous everywhere except at $x$,where $x=\frac{n \pi}{4}$,where $n$ odd numbers.