Exercise 1. Let f: (0, 00) -→ R have the property that lim rf(x) = L, for some real number L. Prove rigorously (using the definition) that lim f (x) = 0.

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A: To prove that for no number C foes limit x tends to c f(x) exist.

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Q: (4) Let f(x) be the function whose domain is all of R given by the rule 42 if r € Z and f(x) = 10…

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Q: Exercise 2. Let f: (1, 00) → R and g : (0, 1) → R be such that g(x) = f(1/x). Prove that lim f(x) =…

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