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## Homework Statement

prove that the product of continuous functions is continous

## Homework Equations

## The Attempt at a Solution

f is continuous for all a. given epilon>0 there exists a delta>0 st |x-a|<delta implies |f(x)-f(a)|< episilon.g is continuous for all a. given epilon>0 there exists a delta2>0 st |x-a|<delta2 implies |g(x)-g(a)|< episilon.|f(x)g(x)-f(a)g(a)|=|f(x)g(x)-f(x)g(a)+f(x)g(a)-f(a)g(a)|...