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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.
PROOF OF VARIOUS LIMIT PROPERTIES In this section we are going to prove several of the fundamental facts and properties about limits which we saw previously. Before proceeding
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