The limit of a product is the product of the limits:
The limit of a quotient is the quotient of the limits:
AKA the "Flyswatter Theorem". Why?
Ratios of Polynomials
The limiting behavior of the ratio of two polynomials depends on the degree of the polynomials. The polynomial of higher degree "wins". If their degrees are the same, then the limit is the ratio of the leading coefficients.
-- DickFurnas - 16 Nov 2008