How do you find the vertical, horizontal or slant asymptotes for #y = (8 x^2 + x - 2)/(x^2 + x - 72)#?
The vertical asymptotes are
and the horizontal asymptote is
We start by factorising the denominator
As we cannot divide by so
So the vertical asymptotes are
As the degree of the polynomial of the numerator and denominator are the same, there is no slant asymptote.
To find the horizontal asymptote, we find the limit as
We take the highest order of the polynomials
So the horizontal asymptote is