2. LEFT AND RIGHT LIMITS (a) Prove that f: (0, 1)→ R defined by f(x) = = is not uniformly continuous. (b) Let f: R\ {0} → R be the function defined by f(x) = sin(). Prove that the left and right limits of f at 0 do not exist. = =x√√1+. Find the left and right (c) Let f: R\ {0} → R be the function defined by f(x) limits of f at 0.

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