# Operations on limit

by quasar987
Tags: limit, operations
 Sci Advisor HW Helper PF Gold P: 4,772 My Real Analysis textbook says: Let f,g: D --> R be two functions of common domain D that posses a limit at x_0 an accumulation point of D. Then, f/g as a limit at x_0 and this limit is the quotient of the limit of f to the limit of g, as long as $g \neq 0 \ \forall x \ \epsilon \ D$ and that the limit of g is not 0. Does this mean that if the limit of g is zero we cannot conclude or could we extend the theorem to: if the limit of g is 0, then the limit of f/g does not exist?