# Finding the vertical asymtope?

• Jul 16th 2011, 12:57 PM
homeylova223
Finding the vertical asymtope?
Can anyone help me find the vertical asymptote of these functions?

f(x)=tan(2x)

f(x)=((x))/((sin(x))
• Jul 16th 2011, 01:15 PM
chisigma
Re: Finding the vertical asymtope?
In both cases there are infinite vertical asymptotes, not only one vertical asymptote...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$
• Jul 16th 2011, 01:36 PM
Siron
Re: Finding the vertical asymtope?
You have to find a number $\displaystyle a$ which:
$\displaystyle \lim_{x \uparrow a} f(x)= \pm \infty$ or $\displaystyle \lim_{x \downarrow a} f(x)= \pm \infty$

So the vertical asymptot will be: $\displaystyle x=a$
• Jul 16th 2011, 11:17 PM
earboth
Re: Finding the vertical asymtope?
Quote:

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:

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

... 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.