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 + (x-6)/(x^2+6x+5)

so as x get larger, (x-6)/(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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