SOLUTION: How do I find the horizontal asymptotes when the powers of x are different in the numerator and the denominator?
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Question 249763: How do I find the horizontal asymptotes when the powers of x are different in the numerator and the denominator? Found 2 solutions by solver91311, jsmallt9:Answer by solver91311(24713) (Show Source):
If the degree of the numerator is larger than the degree of the denominator, then there is no horizontal asymptote. However, if the degree of the numerator differs from the smaller denominator degree by 1, then there is an oblique (or slant) asymptote that is the line described by the quotient of the numerator divided by the denominator excluding any remainder.
If the degree of the numerator is equal to the degree of the denominator, then there is a horizontal asymptote at where is the lead coefficient of the numerator polynomial and is the lead coefficient of the denominator polynomial.
If the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at , which is to say the -axis.
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.)
The degree (highest exponent) of the numerator is less than the degree of the denominator. When this happens y = 0 is the horizontal asymptote.
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
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
(