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.