Posted by fsfsfsfss on Saturday, November 26, 2011 at 6:29pm.
Determine if the graph of the rational function has a slant asymptote. If it does, find the equation of the slant asymptote.
(2x^3+18x^2+47x+24)/(x^2+6x+5)

calculus  Damon, Saturday, November 26, 2011 at 6:42pm
As x gets very large in magnitude this looks like
2 x^3/x^2
or in other words 2x
line with slope of 2
y = 2x

calculus  Damon, Saturday, November 26, 2011 at 7:45pm
Oh, when x = 0
y = 24/5
so
y = 2 x + 24/5

calculus  Reiny, Saturday, November 26, 2011 at 8:16pm
So a long division to get
(2x^3 + 18x^2 + 47x + 24)/ (x^2 + 6x + 5) = 2x + 6 + (x6)/(x^2+6x+5)
so as x get larger, (x6)/(x^2+6x+5)
> 0
and we are left with
y = 2x + 6
So the slant asymptote is y = 2x + 6
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