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Math Help - oblique asymtotes

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by dimeola View Post
    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.
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