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calculus

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f(x)=8x^3+1x^2–8x+2/–7x^2–4x+9

Find the equation of the non-vertical asymptote.
y =

Does f(x) intersect its non-vertical asymptote? (yes or no)
What is the smallest value of x at which f(x) intersects its non-vertical asymptote? ( Enter No in the question blank if you answered no above.) .

  • calculus - ,

    The equation of the non-vertical asymptote can be found by evaluating
    Lim x→±∞ f(x)
    The limit can be found by dividing both the numerator and denominator by x² and is found to be -(8/7)x.
    Thus the equation of the non-vertical asymptote is
    y=-(8/7)x ....(1)

    To find out if f(x) intersects (1) above, we equate
    f(x)=-(8/7)x .....(2)
    and solve for x.
    Since the x³ terms cancel, (2) reduces to a quadratic with roots at
    x=(3*√(46)+8)/25, or
    -(3*√(46)-8)/25
    Make your pick for the leftmost intersection point.

    Check my work.

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