Explore BrainMass

Explore BrainMass

    Algebraic continuity theorem

    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 February 24, 2021, 2:34 pm ad1c9bdddf

    Solution Preview


    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.