Recall the definition of a limit: means given any positive real number, ε, there exists a positive real number, δ, such that
A function, f, is continuous on the open interval (a,b) means for all c in (a,b).
A function, f, is continuous on the closed interval [a,b] means f is continuous on (a,b) and , and .
Calculus Theorems -- important facts about continuous functions
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