Algebraic continuity theorem

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(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.

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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.

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