Finding the vertical asymtope?

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

f(x)=tan(2x)

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

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

Kind regards

You have to find a number which:
or

So the vertical asymptot will be:

Quote:

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Originally Posted by homeylova223

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

f(x)=tan(2x)

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

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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:



... 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.