Recall that f(x)=√√ is continuous over [0, +∞). (a) Show that f(x) = √√ is uniformly continuous over [1,+∞). (b) Show that f(x) = √ is uniformly continuous over [0, 1]. (c) Show that a function that is uniformly continuous over [a, b] and [b, +∞) is uni- formly continuous over [a, +∞). (d) Prove that if {an}neNL where an ≥ 0 for all n, then {√√}neN →√I.

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