Question

Where are the asymptotes of f(x) = tan 2x from x = 0 to x = π?

Answer 1

tan(x) is undefined when x = pi/2 and x = 3pi/2 for 0 < x < 2pi Therefore, tan(2x) is undefined when x = pi/4 and x = 3pi/4 for 0 < x < pi

Answer 2

Answer:

The asymptotes of  $\tan (2x)$  is when   $x=\frac{\pi}{4},\frac{3\pi}{4}$      

Step-by-step explanation:

Given : $f(x)=\tan (2x)$ from $x = 0 \text{ to } x = \pi$

To find : The asymptotes of the function?

Solution :

$f(x)=\tan (2x)$

Re-written as

$f(x)=\tan (2x)=\frac{\sin (2x)}{\cos (2x)}$

Now, we need to find the value of x that makes $\cos(2x)=0$

$\cos(2x)=0$

$2x=\cos^{-1}0$

$2x=\frac{\pi}{2},\frac{3\pi}{2}$

$x=\frac{\pi}{4},\frac{3\pi}{4}$

The function $\cos(2x)$ has a period of $\pi$

So, The asymptote of $\tan (2x)$ is when  $x=\frac{\pi}{4}+\pi n\text{ or }\frac{3\pi}{4}+\pi n$

But from $x = 0 \text{ to } x = \pi$

The asymptotes of  $\tan (2x)$  is when   $x=\frac{\pi}{4},\frac{3\pi}{4}$