calculus

posted by .

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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Find the equation of the non-vertical asymptote. y=?
  2. Math - Calculus

    Find the equation of the non-vertical asymptote. What is the smallest value of x at which f(x) intersects its?
  3. CALCULUS HELP !

    f(x)=(-3x^3-x^2-9x-8)/(6x^2+4x+3. Find the equation of the non-vertical asymptote. y= Does f(x) intersect its non-vertical asymptote ?
  4. CALCULUS!

    f(x)=(6x^3–9x^2–3x–1)/(4x^2+7x–3) . Find the equation of the non-vertical asymptote. y = ____3x/2 - 39/8_____ Does f(x) intersect its non-vertical asymptote?
  5. CALC 2a

    f(x)=x^3-3x^2-3x-8/(-3x^2-4x-6) Find the equation of the non-vertical asymptote. What is the smallest value of x at which f(x) intersects its non-vertical asymptote?
  6. Calc

    f(x)=x^3-3x^2-3x-8/(-3x^2-4x-6) Find the equation of the non-vertical asymptote. What is the smallest value of x at which f(x) intersects its non-vertical asymptote?
  7. CALC

    f(x)=x^3-3x^2-3x-8/(-3x^2-4x-6) Find the equation of the non-vertical asymptote. What is the smallest value of x at which f(x) intersects its non-vertical asymptote?
  8. calc

    f(x)=[5x^3-4x^2-8x+9]/[2x^2-1x-3] Find the equation of the non-vertical asymptote. y = Does f(x) intersect its non-vertical asymptote?
  9. calc

    f(x)=[5x^3-4x^2-8x+9]/[2x^2-1x-3] Find the equation of the non-vertical asymptote. y = Does f(x) intersect its non-vertical asymptote?
  10. Calculus

    f(x)= (-5x^3 + 3x^2 + 3x -5)/(-8x^2 +2x + 7) Find the equation of the non-vertical asymptote. y = ?

More Similar Questions