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Calc

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A rational function f(x) contains quadratic functions in both the numerator and denominator. Also the function f(x) has a vertical asymptote at x=5, a single x intercept of (2,0) and f is removeably discontinuous at x=1 because the lim x-> 1 is -1/9.

Find f(0) and lim x-> infinity of F(x)

  • Calc - ,

    Looks like the function has (x-5) in the denominator, but not the numerator.

    ??/?(x-5)

    It has (x-1) both top and bottom, because it's otherwise continuous there.

    ?(x-1)/(x-1)(x-5)

    x=2 when y=0

    (x-2)(x-1)/(x-1)(x-5)

    limit is -1/9 at x=1

    -4(x-2)(x-1)/9(x-1)(x-5)

    f(0) = -8/45
    as x gets large, f(x) approaches -4/9

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