asymptotes of graph of rational function
Let be a fractional expression where and are polynomials with real coefficients such that their quotient can not be reduced (http://planetmath.org/Division) to a polynomial. We suppose that and have no common zeros.
If the division of the polynomials is performed, then a result of the form
is gotten, where and are polynomials such that
Every zero of the denominator gives a vertical asymptote .
If (i.e. or ) then the graph has the horizontal asymptote .
If then the graph has the skew asymptote .
Proof of 2 and 3. We have as .
Remark. Here we use the convention that the degree of the zero polynomial is .
|Title||asymptotes of graph of rational function|
|Date of creation||2013-03-22 15:09:34|
|Last modified on||2013-03-22 15:09:34|
|Last modified by||eshyvari (13396)|