Posted by Jin on Saturday, September 4, 2010 at 12:18am.
f(x)=8x^3+1x^2–8x+2/–7x^2–4x+9
Find the equation of the nonvertical asymptote.
y =
Does f(x) intersect its nonvertical asymptote? (yes or no)
What is the smallest value of x at which f(x) intersects its nonvertical asymptote? ( Enter No in the question blank if you answered no above.) .

calculus  MathMate, Saturday, September 4, 2010 at 7:53am
The equation of the nonvertical 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 nonvertical 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.