Limits of rational functions
If R (x) = p(x)/ q (x) and the degree of the polynomial p(x) is greater than the degree of q(x), then
If the degree of q(x) is greater than the degree of p(x), then
Finally, if the degree of p(x) is equal to the degree of q(x), then
Remark
We reemphasize that statements such as f (x ) → ∞ as x → a , f (x ) → −∞ as x → a, and f (x ) → ∞ as x → ∞ , f (x ) → −∞ as x → ∞ mean that the limits do not exist. The symbol ∞ does not represent a number and should not be treated as a number.
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