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Math Help - find these horizontal asymptotes without calculator

  1. #1
    Junior Member BugzLooney's Avatar
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    find these horizontal asymptotes without calculator

    y = 9e^x/e^x-4

    I know it is 0 and 9 when I do it in my calculator, but I didn't quite understand algebraically. My professor said the e^x will cancel out but then why doesn't the 4 on the bottom get factored in?
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  2. #2
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    skeeter's Avatar
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    Quote Originally Posted by BugzLooney View Post
    y = 9e^x/e^x-4

    I know it is 0 and 9 when I do it in my calculator, but I didn't quite understand algebraically. My professor said the e^x will cancel out but then why doesn't the 4 on the bottom get factored in?
    divide every term by e^x ...

    y = \frac{9}{1 - \frac{4}{e^x}}

    as x \to \infty , \frac{4}{e^x} \to 0 ... what's left?
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  3. #3
    Junior Member BugzLooney's Avatar
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    Hey yea I think I had it before you posted but thank you. Wanted to make sure though just in case I couldn't.
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