For rational function, limit = HA ?

Test Preparation AP Mathematics & Computer Science
1

<p>Hello!</p>

<p>For rational function f(x)= R(x) / D(x), why do we use rules of horizontal asymtotes to find limit, but not using vertical asymtote?</p>

2

<p>Those rules don’t apply for vertical asymptotes.</p>

<p>For example, suppose that f(x) = (x-3)/(x^2 - 1). lim(x->1) f(x) does not exist / approaches +/- infinity.</p>

<p>However, if f(x) = (x^3 - 3x^2)/(x^2 - 1), lim(x->1) f(x) also does not exist. </p>

<p>For a rational function, the degree of the numerator/denominator has nothing to do with a vertical asymptote. A general rule of thumb is, if you plug in x and obtain c/0 (where c is non-zero), chances are, you have a vertical asymptote. If you obtain 0/0, this is indeterminate, and you cannot claim that there is an asymptote.</p>