1) If g(x) is continuous at c and g(c)>0, show that there is an open interval centered at c on which g(x) is always positive. It makes sense when I read it, I'm confused how I go about proving it.
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Hint : let in the definition of continuity at .
Originally Posted by Janu42 1) If g(x) is continuous at c and g(c)>0, show that there is an open interval centered at c on which g(x) is always positive. It makes sense when I read it, I'm confused how I go about proving it. The definition of continuity. and since this is an open set there exists some and by continuity there exists some such that
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