Let b R and f : R\[b] R be a function. We write limitxb f

Chapter , Problem 31

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Let b R and f : R\[b] R be a function. We write limitxb f (x) = L and say that L is the left-hand limit of f at b if for every > 0 there is a > 0 such that x < b and 0 < |x b| < implies | f (x) L| < . (a) Formulate a definition of right-hand limit, or limitxb+ f (x). (b) Find limitx01/(1 + e1/x ) and limitx0+1/(1 + e1/x ). (c) Sketch the graph of 1/(1 + e1/x )

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