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

f(x)=tan(2x)

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

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- Jul 16th 2011, 12:57 PMhomeylova223Finding 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 PMchisigmaRe: 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 PMSironRe: 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 PMearbothRe: Finding the vertical asymtope?
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.