Let A ~ 1R, let f: A -+ 1R and let c e 1R be a cluster point of A. If lim f exists, and

Chapter 4, Problem 13

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Let A ~ 1R, let f: A -+ 1R and let c e 1R be a cluster point of A. If lim f exists, and if 1/1 x-c denotes the function defined for x e A by 1/1 (x) := 1/(x)l, prove that lim 1/1 =I lim /1 x-c x-c

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