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find the sum of p+m if the function
g(x)= p(x^2-m)/(x+2)(x+5)has a horizontal asymptote at y=5 and a hole at x=-2

  • calculus -

    we know that at large x,

    g(x) =~ 5, so p = 5, giving us

    g(x) = 5(x^2 - m)/(x+2)(x+5)
    A hole at x = -2 means that the numerator is divisible by (x+2) so that

    g(x) = 5(x+2)(x-2)/(x+2)(x+5)
    making m = 4

    p+m = 9

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