Posted by Jin on Saturday, September 4, 2010 at 12:18am.
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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