Question: a) Suppose that f : [0, ) R is continuous and that there is an L R such that f(x) L as

a) Suppose that f : [0, ∞) → R is continuous and that there is an L ∊ R such that f(x) → L as x → ∞. Prove that / is uniformly continuous on [0, ∞).
b) Prove that f(x) = l/(x2 + 1) is uniformly continuous on R.

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