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Math Help - what asymptote ?

  1. #1
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    what asymptote ?

    Hello, I am having issues with an equation involving limits and I am suppose to find the Vertical Asymptote. I thought that this equation had no Vertical asymptotes but mathlab says there is a VA at x=4

    f(x=)  \frac{x^2-9x+20}{x^2-8x+16}

    factor
     \frac{(x-5)(x-4)}{(x-4)(x-4)}
    the (x-4) cancels and leaves
     \frac{(x-5)}{(x-4)}

    which leave a possible assymptote at x = 4,
    but if i plug in 4 to the original equation
     \frac{4^2-9(4)+20}{4^2-8(4)+16} =  \frac{0}{0}
    which is not really an assymptote, but a hole in the graph. What am I doing wrong?
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  2. #2
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    Re: what asymptote ?

    Hi,
    i do see that there is vertical assymptote.please find below the reasoning
    1> Vertical asymptotesThe line x = a is a vertical asymptote of the graph of the function y = (x) if at least one of the following statements is true:

    a.lim x-> afor f(x) = + or - infinity
    b.lim x-> -afor f(x) = + or - infinity.
    2.keeping the first point in mind and applying L-Hospital's rule for f(x) it becomes (2x-9)/(2x-8).then put x=4 we get -1/0= -infinity
    3.L-Hospital's rule;is a rule for converting an indeterminent form of functions (i.e 0/0,infinity/infinity,o^infinity,infinity^0,infinity-infinity......)into diterminent forms by differentiating the given function.
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