# Thread: Finding the vertical asymtope?

1. ## Finding the vertical asymtope?

Can anyone help me find the vertical asymptote of these functions?

f(x)=tan(2x)

f(x)=((x))/((sin(x))

2. ## Re: Finding the vertical asymtope?

In both cases there are infinite vertical asymptotes, not only one vertical asymptote...

Kind regards

$\chi$ $\sigma$

3. ## Re: Finding the vertical asymtope?

You have to find a number $a$ which:
$\lim_{x \uparrow a} f(x)= \pm \infty$ or $\lim_{x \downarrow a} f(x)= \pm \infty$

So the vertical asymptot will be: $x=a$

4. ## Re: Finding the vertical asymtope?

Originally Posted by homeylova223
Can anyone help me find the vertical asymptote of these functions?

f(x)=tan(2x)

f(x)=((x))/((sin(x))
1. If a function is the quotient of functions (as it is in your case) you'll find a vertical asymptote if the denominator function equals zero and the numerator function is not zero.

2. Re-write the first function:

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

... and now apply the hint from #1 to find at least one of the unlimited number of vertical asymptotes.

3. Do the same with the 2nd question but be aware that the hint at #1 doesn't work if x approaches zero.