Find the equation of the non-vertical asymptote.
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 - MathMate, Saturday, September 4, 2010 at 7:53am
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
To find out if f(x) intersects (1) above, we equate
and solve for x.
Since the x³ terms cancel, (2) reduces to a quadratic with roots at
Make your pick for the leftmost intersection point.
Check my work.