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5. Let I be an open interval with a ∈ I and suppose that f is...

5. Let I be an open interval with a ∈ I and suppose that f is a function defined on I\{a} where the limit of f exists as x → a and L = limx→a f(x). Prove that the limit of |f| exists as x → a and |L| = limx→a |f(x)|. Is the converse true? Prove or furnish a counterexample.

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