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 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 -
**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

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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