Algebraic continuity theorem

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

(Algebraic continuity theorem): Assume f:A->R and g:A->R are continuous at a point c belong to A)then f(x)/g(x) is continuous at c, if both f and g are provided that the quotient is defined, show that if g is continuous at c and g(c) not= 0 then there exists an open interval containing c on which f(x)/g(x) is always defined.

© BrainMass Inc. brainmass.com November 30, 2021, 12:14 am ad1c9bdddf
https://brainmass.com/math/basic-algebra/algebraic-continuity-theorem-29169

Solution Preview

Proof:

Since g(c) not=0 and g is continuous at c, we have two cases: g(c)>0 or g(c)<0. Without loss of generality, suppose ...

Solution Summary

(Algebraic continuity theorem): This is a proof showing there exists an open interval on which f(x)/g(x) is always defined.

$2.49