Question 249763
There are three possible situations:<ul><li>The degree (highest exponent) of the numerator is greater than the degree of the denominator. When this happens there is no horizontal asymptote. (There could be an oblique asymptote.)</li><li>The degree (highest exponent) of the numerator is less than the degree of the denominator. When this happens y = 0 is the horizontal asymptote.</li><li>The degrees of the numerator and denominator are the same. In this case the horizontal asymptote will be y = (the ratio of the leading coefficients). For example, if
{{{y = (6x^12 +34x^6 + 12x -900)/(5x^12 - 500x^11 + 78x^3 -20000)}}}
The degrees of the numerator and denominator are both 12. The leading coefficients (the coefficients of the highest power terms) are 6 and 5 respectively. The horizontal asymptote will be:
y = 6/5</li></ul>