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Math Help - Finding the vertical asymtope?

  1. #1
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    Finding the vertical asymtope?

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

    f(x)=tan(2x)

    f(x)=((x))/((sin(x))
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  2. #2
    MHF Contributor chisigma's Avatar
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    Re: Finding the vertical asymtope?

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

    Kind regards

    \chi \sigma
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  3. #3
    MHF Contributor Siron's Avatar
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    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
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  4. #4
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    Re: Finding the vertical asymtope?

    Quote Originally Posted by homeylova223 View Post
    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.
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