Math Help - oblique asymtotes

1. oblique asymtotes

Hi all,

For the ciurve : f (x ) = (x-1)^3 / (x+1)^2

Can I said that the line y = x -5 is its oblique asymtotes?

seems this line y = x-5 intersect with f(x) in points between -1< x < 0

2. Originally Posted by dimeola
Hi all,

For the ciurve : f (x ) = (x-1)^3 / (x+1)^2

Can I said that the line y = x -5 is its oblique asymtotes?

seems this line y = x-5 intersect with f(x) in points between -1< x < 0
your answer is correct although i have no idea how you got it! there's a very easy way to find oblique (or slant) asymtotes: long division! we have:

$\frac{(x-1)^3}{(x+1)^2} = x - 5 + \frac{12x + 4}{(x+1)^2}.$ now since $\lim_{x\to\infty} \frac{12x+4}{(x+1)^2}=0,$ the oblique asymptote is $y=x-5.$