Convergence, Mathematics

Assume that (xn) is a sequence of real numbers and that a, b € R with a is not eaqual to 0.

(a) If (xn) converges to x, show that (|axn + b|) converges to |ax + b|.
(b) Give an instance , with brief justi cation, where (|xn|) converges but (xn) does not.
(c) If (|xn|) converges to 0, elustratethat (xn) converges to 0.

In (a) you need to use only the de nition of convergence and no other limit theorems.

Posted Date: 3/21/2013 3:11:19 AM | Location : United States







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