Calculus/Asymptotes

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Expert: - 9/11/2008


Question
Given the function of f(x), determine all asymptotes and explain or show why and where they occur.

f(x) = x^2 + x - 2
      -----------
      x^3 - 6x^2 + 5x

Answer
An assymptote is a line that is approached but never crossed.
Start by factoring the equation.  The top is (x+2)(x-1).  The bottom is x(x-1)(x-6).

This says that one of that assymptotes is x=6, since the graph can't cross that value and goes to plus or minus infinity.  It also says there is an assymptote at x=0.  At x=1, it is not an assymptote since the numerator also has the factor x-1.  It is just a nonexistant point.

There will also be a vretical assymptote at x=0 due to the fact that the factor of x in the denominator is 1 higher than the biggest power in the numerator.

Calculus

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