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Finding Equations of Asymptotes

The easiest asymptotes to find are those which result from the factorisation of the denominator.

Ifthen there are asymptotes at

An asymptote that results from the highest power ofin the numerator being one larger than the highest power ofin the denominator or vice versa is also easily found.

- find the equations of the asymptotes.

We divide top and bottom byand take the limit as

The equation of one asymptote isand the equation of the other issince the denominator has a root at

– find the equations of the asymptotes.

we divide top and bottom byand take the limit as

The equation of one asymptote isand the equation of the other issince the denominator has a root at

If the power ofin the denominator is higher than the power ofin the numerator than there is always an asymptote at

- find the equations of the asymptotes.

We divide top and bottom byand take the limit as

The equation of one asymptote isand the equation of the other issince the denominator has a root at

If the highest powers ofin numerator and denominator are the same then there is an asymptote at the quotient of these coefficients.