Calculus

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Let
f(x)=(4x^2 -7x +2)/(x^2 -16x +63)

Find the equations of the horizontal asymptotes and the vertical asymptotes of f(x). If there are no asymptotes of a given type, enter NONE. If there is more than one asymptote of a given type, give a comma separated list (i.e.: 1, 2,...).

  • Calculus - asymptotes -

    To find the vertical asymptotes, factorize the denominator (if possible) and determine the zeroes of the denominator. Here we find two at x=7 and x=9:
    f(x)=(4x^2 -7x +2)/(x^2 -16x +63)
    =(4x^2 -7x +2)/((x-7)(x-9))

    To find horizontal asymptotes, find the limit of the function as x->∞ or x->-∞.
    Lim f(x) x->∞
    =Lim (4x²-7x+2)/(x²-16x+63)
    =LIm (4x²/x²)
    =4
    Here we found a horizontal aysmptote at y=4

  • Calculus -

    find the vertical asymptotes of the graph of the function

    g(x) = (4+X)/(X^2 (9-XX)

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