How do you use limits to find a horizontal asymptote?

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Answer 1 · 2018-03-17T16:35:39

Please see below.

We find limit of the function $f(x)$ as $x->oo$ i.e. $y=lim_(x->oo)f(x)$ . An example is shown below.

Let the function be $f(x)=(ax^3+bx^2+cx+d)/(px^3+qx^2+rx+s)$ ,

then $lim_(x->oo)(ax^3+bx^2+cx+d)/(px^3+qx^2+rx+s)$ .

Now dividing numerator and denominator by $x^3$ , we get

$lim_(x->oo)(a+b/x+c/x^2+d/x^3)/(p+q/x+r/x^2+s/x^3)$

= $a/p$

and hence horizontal asymptote is $y=a/p$